Two goals by Nikica Jelavic continued Everton's flying start to the season as David Moyes's side came from behind to seal a fourth win in six league games.
Record £12m signing Gaston Ramirez gave Southampton the lead at Goodison with a header from Adam Lallana's corner.
But Leon Osman levelled from eight yards after a cross by Kevin Mirallas, who then threaded a pass for Croatian striker Jelavic to make it 2-1.
Jelavic cemented victory with a header after good work by Seamus Coleman.
While Southampton have now conceded an alarming 18 goals in six Premier League games, Everton's latest success adds weight to the belief that Moyes's men can challenge for Champions League qualification.
The hosts, now up to second in the table, displayed great character to recover from a desperate start to score all three goals in the space of 13 first-half minutes and leave the Saints longing for the half-time whistle.
On the eve of the match, Moyes, in the final year of his Goodison Park contract, ruled out imminent discussions to resolve his long-term future, the Scot insisting he was more concerned with concentrating on his team's healthy start than sorting out his own future.
But Blues fans will be anxious chairman Bill Kenwright secures Moyes's signature in the coming weeks before another club comes knocking for the 49-year-old.
Everton's sixth win in seven home league games was achieved the hard way after the Saints took a shock lead.
Everton's flying start
This is Everton's best start to a Premier League season after six games since the 2004-05 campaign - when they finished fourth
While Moyes will be delighted to start October near the Premier League summit, he will have been unimpressed with the shabby defending that allowed Ramirez, who was totally unmarked, to head Lallana's sixth minute corner beyond Tim Howard.
John Heitinga was presented with a chance to equalise moments later but headed straight at keeper Paulo Gazzaniga before Jay Rodriguez flashed the ball across the face of the Toffees' six-yard area in a thoroughly entertaining clash.
It proved a costly miss by the former Burnley man, Everton regrouping to turn the game upside down with three quick goals.
Midfielder Osman lashed the ball home from eight yards after the Southampton defence made a hash of trying to clear Mirallas's dangerous cross.
With Marouane Fellaini oozing confidence and Jelavic in fine form, it was only a matter of time before the hosts took the lead.
Jelvavic made it 2-1 from an acute angle after Mirallas's beautifully threaded pass.
The former Rangers man then netted his third league goal of the season, a powerful header at the back post which Gazzaniga got a hand to but could not keep out.
Southampton rallied after half-time - Rickie Lambert and Ramirez both going close.
But the Toffees were worthy winners, Fellaini heading against the bar before Osman and Mirallas both went close to increasing the lead.
Everton, notorious slow starters, are helping set the pace heading into October.
- 24 Howard
- 03 Baines
- 05 Heitinga
- 06 Jagielka
- 18 Neville
- 23 Coleman
- 21 Osman (Distin - 90' )
- 22 Pienaar
- 25 Fellaini
- 07 Jelavic (Anichebe - 77' )
- 11 Mirallas (Oviedo - 80' )
- 01 Mucha
- 15 Distin
- 34 Duffy
- 08 Oviedo
- 19 Gueye
- 27 Vellios
- 28 Anichebe
- 12 Gazzaniga
- 02 Clyne (Reeves - 81' )
- 03 Yoshida
- 06 Fonte
- 22 Richardson
- 08 S Davis
- 10 Ramirez
- 16 Ward-Prowse
- 20 Lallana (Chaplow - 90' )
- 07 Lambert
- 09 Rodriguez (Mayuka - 81' )
- 01 K Davis
- 05 Hooiveld
- 29 Reeves
- 21 Guly
- 27 Chaplow
- 42 Puncheon
- 24 Mayuka
Live Text Commentary
Outswinging corner taken by Leighton Baines from the left by-line, clearance by Jose Fonte.90:00 +1:13
Paulo Gazzaniga takes the free kick.90:00 +1:13 Substitution
Substitution Sylvain Distin comes on in place of Leon Osman.90:00 +1:13
Leighton Baines concedes a free kick for a foul on Steven Davis.89:27 Substitution
Substitution Richard Chaplow on for Adam Lallana.89:19
A cross is delivered by James Ward-Prowse.88:53
Effort from the edge of the box by Marouane Fellaini goes wide of the right-hand upright.80:47 Substitution
Substitution Ben Reeves is brought on as a substitute for Nathaniel Clyne.80:47 Substitution
Substitution Emmanuel Mayuka is brought on as a substitute for Jay Rodriguez.79:15 Substitution
Substitution Kevin Mirallas leaves the field to be replaced by Bryan Oviedo.78:53
Leon Osman takes a shot.78:17
Marouane Fellaini takes a shot. Maya Yoshida gets a block in.77:05
Foul by Kevin Mirallas on Adam Lallana, free kick awarded. Nathaniel Clyne restarts play with the free kick.76:11 Full time
Full Time The match has reached full-time.71:23
Marouane Fellaini takes a shot. Paulo Gazzaniga makes a save.70:13
Johnny Heitinga fouled by Gaston Ramirez, the ref awards a free kick. Johnny Heitinga restarts play with the free kick.69:16
Gaston Ramirez produces a right-footed shot from deep inside the penalty box which goes wide of the left-hand upright.68:11
Gaston Ramirez takes a shot. Save by Tim Howard.67:22
Steven Pienaar takes a short corner.67:08
Kevin Mirallas takes a shot. Save by Paulo Gazzaniga.
Jay Rodriguez takes a shot. Tim Howard makes a save.65:10
The assistant referee signals for offside against Nikica Jelavic. Free kick taken by Paulo Gazzaniga.63:54
A cross is delivered by Nikica Jelavic.63:29
Jay Rodriguez takes a shot.61:05 Substitution
Substitution Victor Anichebe on for Nikica Jelavic.61:05
Effort from the edge of the box by Marouane Fellaini goes wide of the left-hand post.59:12
Shot from just outside the area by Leon Osman misses to the right of the target.58:35
Outswinging corner taken by Leighton Baines, Header from deep inside the penalty area by Nikica Jelavic goes harmlessly over the crossbar.58:12
Outswinging corner taken by Leighton Baines from the left by-line played to the near post, clearance by Jose Fonte.51:15
Corner from right by-line taken by Kevin Mirallas.46:09 +4:09
Corner taken by Leighton Baines from the left by-line.45:13 +4:09
Corner from right by-line taken by Leighton Baines.45:01
The second half kicks off.45:00 +35:01 Half time
Half Time The match has reached half-time.43:52
The assistant referee signals for offside against Rickie Lambert. Phil Neville takes the indirect free kick.43:33
Seamus Coleman produces a cross, Marouane Fellaini takes a shot. Save made by Paulo Gazzaniga.41:24
Kevin Mirallas produces a cross, clearance made by Maya Yoshida.40:23
A cross is delivered by Nathaniel Clyne, Leon Osman manages to make a clearance.38:57
Inswinging corner taken right-footed by Adam Lallana from the right by-line to the near post, clearance by Johnny Heitinga.37:09
Assist by Seamus Coleman.37:09 Goal scored
Goal! - Nikica Jelavic - Everton 3 - 1 Southamp'n Nikica Jelavic scores a headed goal from deep inside the penalty area. Everton 3-1 Southampton.37:07
Centre by Seamus Coleman,36:47
The ball is delivered by Leighton Baines, Nikica Jelavic takes a shot. Save by Paulo Gazzaniga.35:37
Nikica Jelavic is caught offside. Free kick taken by Paulo Gazzaniga.34:40
The ball is swung over by Leighton Baines, Jose Fonte makes a clearance.34:07
Inswinging corner taken right-footed by Steven Pienaar from the left by-line, clearance by Jose Fonte.33:27
Handball by Nathaniel Clyne. Leighton Baines delivers the ball from the free kick left-footed from right wing, Rickie Lambert manages to make a clearance.31:57
Assist on the goal came from Kevin Mirallas.31:57 Goal scored
Goal! - Nikica Jelavic - Everton 2 - 1 Southamp'n Nikica Jelavic finds the net with a goal from the edge of the penalty box to the bottom right corner of the goal. Everton 2-1 Southampton.30:53
The referee blows for offside against Kevin Mirallas. Paulo Gazzaniga takes the free kick.29:31
Nathaniel Clyne concedes a free kick for a foul on Kevin Mirallas. Free kick taken by Phil Jagielka.28:14
The ball is crossed by Marouane Fellaini.27:54
The ball is sent over by Seamus Coleman, Frazer Richardson manages to make a clearance.26:43
Nikica Jelavic has an effort at goal from just inside the box that misses to the left of the target.24:42
Assist on the goal came from Nikica Jelavic.24:42 Goal scored
Goal! - Leon Osman - Everton 1 - 1 Southamp'n Leon Osman fires in a goal from deep inside the penalty box to the top right corner of the goal. Everton 1-1 Southampton.23:28
Unfair challenge on Johnny Heitinga by Gaston Ramirez results in a free kick. Johnny Heitinga takes the free kick.22:31
The ball is swung over by Marouane Fellaini, clearance by Adam Lallana.21:22
Inswinging corner taken by Gaston Ramirez, Headed effort from inside the area by Rickie Lambert misses to the left of the goal.21:11
James Ward-Prowse sends in a cross, clearance by Phil Jagielka.20:04
The ball is delivered by Rickie Lambert.17:20
Shot from just outside the area by Gaston Ramirez goes over the bar.16:31
Frazer Richardson sends in a cross, clearance by Phil Jagielka.15:47
Adam Lallana sends in a cross.12:52
Marouane Fellaini sends in a cross, Header from deep inside the penalty area by Leon Osman goes harmlessly over the crossbar.10:53
Effort from the edge of the area by Gaston Ramirez goes wide of the left-hand post.8:34
Corner taken left-footed by Leighton Baines from the left by-line, Johnny Heitinga takes a shot. Save by Paulo Gazzaniga.7:30
Corner taken by Leighton Baines from the right by-line, clearance by Gaston Ramirez.5:37
The assist for the goal came from Adam Lallana.5:37 Goal scored
Goal! - Gaston Ramirez - Everton 0 - 1 Southamp'n Gaston Ramirez scores a headed goal from inside the six-yard box. Everton 0-1 Southampton.5:09
Inswinging corner taken by Adam Lallana from the left by-line,4:06
Nikica Jelavic is caught offside. Jose Fonte takes the free kick.3:01
Seamus Coleman crosses the ball.2:16
Nathaniel Clyne crosses the ball.1:44
Shot by Kevin Mirallas from deep inside the penalty area misses to the left of the target.1:29
Leighton Baines produces a cross, Jose Fonte makes a clearance.0:00
The referee gets the game started.
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