By Phil McNultyBBC Sport chief football writer at Anfield
Arsenal secured their first victory of the season in impressive style at Anfield as they won comfortably against a desperately poor Liverpool.
Arsene Wenger's summer signings
scored their first goals for the club either side of the interval to leave new manager Brendan Rodgers presiding over Liverpool's worst start since 1962-63.
Arsenal had the game's outstanding performers in Cazorla and Abou Diaby and a third successive clean sheet will also have delighted Wenger and his new right-hand man Steve Bould.
These are crucial early days for Rodgers and their next league test is a difficult trip to Sunderland.
Raheem Sterling, just 17, offered moments of hope for Liverpool but they were few and far between as more experienced and illustrious team-mates failed to exert any influence over affairs.
Arsenal were dominant in all areas, with Diaby ruling midfield and Cazorla proving what a bargain he is after a £15m move from Malaga.
For two managers who pride themselves on the passing game, Rodgers and Wenger will have been aghast at the number of careless passes and errors that littered an undistinguished first period.
And it was from one such moment of careless, with Liverpool captain Steven Gerrard the culprit, that Arsenal took the lead after 31 minutes.
Gerrard conceded possession as he tried to find Luis Suarez, allowing Cazorla to surge forward and play in Podolski for a clinical finish that the German striker took with great expertise.
Liverpool's poor form
Liverpool have won just one of the last 11 league meetings against Arsenal.
The Reds have won only one of their last seven league games at Anfield - a victory over Chelsea at the end of last season.
The last time Liverpool failed to win at least one of their opening three Premier League games was in 2003.
In among the mediocrity surrounding him, Sterling was again creating a good impression and he almost produced an equaliser with a neat turn inside the box and a powerful shot against the outside of an upright.
The power of Diaby was a feature of the first half and another run through the heart of Liverpool's defence should have brought a second Arsenal goal, only for Olivier Giroud to somehow sweep a simple opportunity wide.
Liverpool appealed for a penalty when Suarez clashed with Per Mertesacker, who had been booked early on after another collision with the Uruguayan, but referee Howard Webb angered The Kop by waving play on.
Reina needed to be alert to block a shot from Kieran Gibbs at his near post and from Carl Jenkinson's long-range effort.
Suarez was fighting a lone battle against Mertesacker and Thomas Vermaelen but at least offered Liverpool some hope with a rising drive that was touched over by Vito Mannone.
This was snuffed out when Cazorla added Arsenal's second after 69 minutes. The Spaniard's shot carried plenty of power but Reina should have done much better than merely help it into the net.
Liverpool's lack of threat will have alarmed Rodgers but at least substitute Jonjo Shelvey, on for debutant Nuri Sahin, was prepared to test Mannone, twice bringing saves with efforts from distance.
Anfield was deserting rapidly as the final whistle was blown - optimism for Wenger and a desperately poor start for Rodgers.
Arsenal manager Arsene Wenger:
"The sharpness gets better from game to game and we looked solid and scored two good goals.
Wenger delights in 'convincing' win
"I believe it is encouraging, playing at two difficult away games so I am pleased. We missed opportunities on the counter-attack at the start of the game but we had a convincing team performance. As long as you don't concede, everyone feels better but I credit the whole team.
"Abou Diaby gets better every game but we need to be cautious with him because he has had so many injuries. He can have a little breather in the international break.
"Everybody understood quickly Cazorla would not need six months to settle. Lukas Podolski is deadly when he gets a chance. I am pleased for them."
Luis Suarez gives away a free kick for an unfair challenge on Vassiriki Diaby. Direct free kick taken by Vito Mannone.
Short corner taken by Steven Gerrard. The ball is delivered by Steven Gerrard, clearance by Olivier Giroud.
Free kick taken by Clarindo Andre Santos.
90:00 +0:55 Booking
Booking The referee shows Jonjo Shelvey a yellow card for unsporting behaviour.
Unfair challenge on Aaron Ramsey by Jonjo Shelvey results in a free kick.
Inswinging corner taken by Steven Gerrard from the left by-line, clearance by Clarindo Andre Santos.
Substitution Thomas Vermaelen leaves the field to be replaced by Laurent Koscielny.
Drilled right-footed shot by Jonjo Shelvey. Vito Mannone makes a save.
Luis Suarez conjures a right-footed shot from inside the six-yard box that clears the bar.
Corner taken right-footed by Steven Gerrard, clearance by Clarindo Andre Santos.
Substitution Lukas Podolski goes off and Clarindo Andre Santos comes on.
Shot by Stewart Downing. Blocked by Kieran Gibbs.
Shot by Jonjo Shelvey. Save made by Vito Mannone.
Centre by Glen Johnson, clearance by Thomas Vermaelen.
Steven Gerrard gives away a free kick for an unfair challenge on Mikel Arteta. Mikel Arteta restarts play with the free kick.
Corner taken by Santi Cazorla played to the near post, Olivier Giroud has a headed effort from close range and clears the crossbar.
A cross is delivered by Steven Gerrard, Kieran Gibbs makes a clearance.
Corner taken right-footed by Steven Gerrard from the left by-line, clearance by Clarindo Andre Santos.
Substitution Clarindo Andre Santos comes on in place of Lukas Podolski.
Stewart Downing produces a curled left-footed shot from 20 yards. Kieran Gibbs gets a block in.
Jonjo Shelvey delivers the ball, clearance by Thomas Vermaelen.
The assistant referee flags for offside against Sanchez Jose Enrique. Mikel Arteta takes the indirect free kick.
Corner taken right-footed by Santi Cazorla to the near post, Foul by Thomas Vermaelen on Jose Reina, free kick awarded. Jose Reina restarts play with the free kick.
Raheem Sterling produces a cross, clearance made by Per Mertesacker. Jonjo Shelvey produces a right-footed shot from just outside the box that goes wide right of the goal.
Substitution Aaron Ramsey joins the action as a substitute, replacing Alex Oxlade-Chamberlain.
Glen Johnson sends in a cross, save by Vito Mannone.
Kieran Gibbs challenges Stewart Downing unfairly and gives away a free kick. Glen Johnson takes the direct free kick.
Assist by Lukas Podolski.
67:19 Goal scored
Goal - Santi Cazorla - Liverpool 0 - 2 Arsenal Santi Cazorla gets on the score sheet with a goal from close in to the top left corner of the goal. Liverpool 0-2 Arsenal.
Substitution Jonjo Shelvey comes on in place of Nuri Sahin.
Santi Cazorla produces a left-footed shot from just outside the box that goes wide right of the goal.
Centre by Raheem Sterling, Stewart Downing has a headed effort at goal from deep inside the area missing to the right of the target.
The ball is crossed by Steven Gerrard, Vito Mannone makes a save.
Stewart Downing takes a shot. Blocked by Thomas Vermaelen. Outswinging corner taken by Steven Gerrard from the right by-line, clearance made by Per Mertesacker.
Mikel Arteta fouled by Stewart Downing, the ref awards a free kick. Vito Mannone restarts play with the free kick.
Shot by Daniel Agger from 35 yards. Save by Vito Mannone.
Carl Jenkinson takes a shot. Jose Reina makes a save.
Luis Suarez produces a drilled right-footed shot from 18 yards. Save by Vito Mannone. Corner taken by Nuri Sahin, clearance made by Lukas Podolski.
Inswinging corner taken right-footed by Steven Gerrard played to the near post, clearance made by Olivier Giroud.
Inswinging corner taken left-footed by Stewart Downing from the right by-line to the near post, Olivier Giroud makes a clearance.
Substitution Fabio Borini leaves the field to be replaced by Stewart Downing.
The ball is crossed by Fabio Borini, clearance by Carl Jenkinson. Sanchez Jose Enrique takes a shot from just inside the penalty box which clears the bar.
Kieran Gibbs takes a shot. Save made by Jose Reina.
Steven Gerrard delivers the ball.
Sanchez Jose Enrique challenges Alex Oxlade-Chamberlain unfairly and gives away a free kick. Vito Mannone restarts play with the free kick.
Mikel Arteta takes the direct free kick.
Booking Martin Skrtel is shown a yellow card for unsporting behaviour.
Free kick awarded for an unfair challenge on Vassiriki Diaby by Martin Skrtel.
Santi Cazorla takes a shot. Daniel Agger gets a block in.
The second half kicks off.
45:00 +2:35 Half time
Half Time The match has reached half-time.
Fabio Borini gives away a free kick for an unfair challenge on Lukas Podolski. Direct free kick taken by Vito Mannone.
Sanchez Jose Enrique produces a cross, Thomas Vermaelen manages to make a clearance.
Glen Johnson crosses the ball, save by Vito Mannone.
Thomas Vermaelen concedes a free kick for a foul on Nuri Sahin. Joe Allen takes the free kick.
Nuri Sahin challenges Mikel Arteta unfairly and gives away a free kick. The free kick is delivered right-footed by Santi Cazorla from right channel, clearance by Glen Johnson.
The offside flag is raised against Raheem Sterling. Vito Mannone restarts play with the free kick.
Effort from deep inside the area by Olivier Giroud misses to the left of the goal.
Fabio Borini takes a shot. Blocked by Thomas Vermaelen.
Mikel Arteta challenges Joe Allen unfairly and gives away a free kick. Direct free kick taken by Sanchez Jose Enrique.
Shot from close in by Raheem Sterling misses to the left of the target.
Corner taken right-footed by Steven Gerrard from the left by-line, Thomas Vermaelen manages to make a clearance. Inswinging corner taken from the left by-line by Steven Gerrard, Lukas Podolski makes a clearance.
Luis Suarez gives away a free kick for an unfair challenge on Mikel Arteta. Direct free kick taken by Mikel Arteta.
Vassiriki Diaby delivers the ball, clearance by Martin Skrtel.
Steven Gerrard sends in a cross, clearance made by Per Mertesacker.
Lukas Podolski takes a shot. Save made by Jose Reina.
Assist by Santi Cazorla.
30:08 Goal scored
Goal - Lukas Podolski - Liverpool 0 - 1 Arsenal Lukas Podolski grabs a goal from close range to the bottom right corner of the goal. Liverpool 0-1 Arsenal.
Luis Suarez takes the direct free kick. Right-footed shot by Steven Gerrard.
Booking Mikel Arteta booked for unsporting behaviour.
Raheem Sterling fouled by Mikel Arteta, the ref awards a free kick.
The ball is sent over by Kieran Gibbs, clearance by Sanchez Jose Enrique. Free kick awarded for an unfair challenge on Jose Reina by Olivier Giroud. Direct free kick taken by Jose Reina.
Santi Cazorla fouled by Sanchez Jose Enrique, the ref awards a free kick. Free kick taken by Mikel Arteta.
Free kick awarded for an unfair challenge on Alex Oxlade-Chamberlain by Luis Suarez. Free kick taken by Thomas Vermaelen.
The ball is crossed by Kieran Gibbs, Martin Skrtel manages to make a clearance.
Long range effort by Thomas Vermaelen goes wide right of the net.
Foul by Fabio Borini on Kieran Gibbs, free kick awarded. The free kick is delivered right-footed by Santi Cazorla from left wing, Steven Gerrard makes a clearance.
Luis Suarez produces a header from deep inside the six-yard box that clears the crossbar.
The ball is crossed by Fabio Borini, clearance by Thomas Vermaelen.
Steven Gerrard takes a outswinging corner.
Santi Cazorla takes a shot. Save by Jose Reina.
The ball is crossed by Lukas Podolski, clearance by Sanchez Jose Enrique.
Effort from the edge of the box by Fabio Borini goes wide of the right-hand upright.
The assistant referee flags for offside against Glen Johnson. Kieran Gibbs takes the free kick.
Luis Suarez produces a strike on goal direct from the free kick.
Booking Caution for Per Mertesacker.
Free kick awarded for an unfair challenge on Luis Suarez by Per Mertesacker.
Shot from just outside the penalty box by Fabio Borini misses to the left of the target.
Olivier Giroud is ruled offside. Jose Reina takes the free kick.
The match has kicked off.
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