Papiss Cisse could not add to Ba's goal when he missed a first-half penalty.
Pardew hopes Ba form continues
Wes Hoolahan and Andrew Surman wasted chances for Norwich, who have yet to win in the league this season.
It was a deserved victory for Newcastle, who should have won more convincingly, while Hughton,
who was sacked as Magpies manager in December 2010
despite leading them to promotion months earlier, will be concerned by his side's ongoing problems in front of goal.
The Canaries, who lost defender Sebastien Bassong to a hamstring injury after just six minutes, did create some decent chances but their composure was missing - something that cannot be said about Ba at the moment.
The 27-year-old striker, whose agent upset manager Alan Pardew with comments suggesting Ba
may want a move away from Newcastle,
scored against the run of play with a well-worked goal which was direct in definition but exquisite in its execution.
Magpies down Canaries
This was Newcastle's first win in four Premier League matches and their first 1-0 victory since March, when Norwich were their victims.
Goalkeeper Steve Harper, deputising for the injured Tim Krul, rolled the ball out to Ben Arfa who glided forward before splitting the Norwich defence with a sublime pass which Ba latched onto and, with his second touch, clinically placed the ball past John Ruddy and into the back of the net.
The goal summed up much of Newcastle's play, with Ben Arfa regularly picking the ball up in the deep and causing the Canaries defence problems with his mixture of inch-perfect passing and mazy dribbling.
The French midfielder almost set up Ba and Cisse on two other occasions - with the Senegalese pair experiencing contrasting fortunes.
While Ba appeared to be buoyed by his strike, his partner is now without a goal in six matches this season.
Hughton seeks winning 'formula'
And his effort for the penalty, won when Mike Williamson was backed into and knocked over by Steve Morison, summed up his day - the ball never threatening the goal as it soared high into the stand.
Hughton's decision to bring in Hoolahan and Morison to replace Grant Holt and Simeon Jackson did not bear dividends, and the Canaries have now scored only twice in five Premier League matches.
Left-back Javier Garrido was their best attacking option, with the former Manchester City man creating two useful chances for Hoolahan and Robert Snodgrass, but they struggled to assert themselves after they had fallen behind.
Their best chance came at the beginning of the second half when Harper denied Andrew Surman after the midfielder had been put clean through on goal.
Hughton sent on Holt and Jackson, but it was the hosts who looked more threatening in the final stages as Ba was put through by Cabaye and saw his shot saved by Ruddy before the keeper denied Gabriel Obertan in stoppage time.
Victory moves Newcastle up to 10th in the Premier League table while Norwich, who face Liverpool, Chelsea and Arsenal in their next three league games, remain just above the relegation zone.
Full Time The referee signals the end of the game.
The ball is swung over by Russell Martin, Cheick Tiote manages to make a clearance.
Short corner worked by Yohan Cabaye.
Gabriel Obertan takes a shot. Save made by John Ruddy.
John Ruddy takes the direct free kick.
Booking Cheick Tiote receives a caution for unsporting behaviour.
Cheick Tiote challenges Michael Turner unfairly and gives away a free kick.
Steve Harper restarts play with the free kick.
Booking Jonathan Howson is shown a yellow card.
Free kick awarded for an unfair challenge on Cheick Tiote by Jonathan Howson.
Inswinging corner taken from the right by-line by Robert Snodgrass.
A cross is delivered by Grant Holt, James Perch makes a clearance.
The free kick is delivered right-footed by Yohan Cabaye from right channel, Grant Holt makes a clearance.
Substitution Shola Ameobi joins the action as a substitute, replacing Hatem Ben Arfa.
Bradley Johnson gives away a free kick for an unfair challenge on Yohan Cabaye.
Demba Ba takes a shot. Save by John Ruddy.
Direct free kick taken by Javier Garrido.
Substitution Simeon Jackson replaces Andrew Surman.
Free kick awarded for an unfair challenge on Robert Snodgrass by Cheick Tiote.
Foul by Grant Holt on Steven Taylor, free kick awarded. Steve Harper takes the direct free kick.
Russell Martin crosses the ball.
Robert Snodgrass concedes a free kick for a foul on Jonas Gutierrez. Direct free kick taken by Steve Harper.
Gabriel Obertan produces a cross.
Foul by Andrew Surman on Yohan Cabaye, free kick awarded. Yohan Cabaye restarts play with the free kick.
Demba Ba concedes a free kick for a foul on Michael Turner. Bradley Johnson takes the direct free kick.
Free kick taken by Steve Harper.
Substitution Vurnon Anita goes off and Cheick Tiote comes on.
Unfair challenge on Jonas Gutierrez by Grant Holt results in a free kick.
Yohan Cabaye takes a shot. Blocked by Leon Barnett.
A cross is delivered by Jonathan Howson, Vurnon Anita makes a clearance.
Wesley Hoolahan sends in a cross, Header from close in by Andrew Surman misses to the right of the goal.
Substitution (Norwich) makes a substitution, with Grant Holt coming on for Steve Morison.
Substitution Papiss Cisse goes off and Gabriel Obertan comes on.
A cross is delivered by Vurnon Anita, Headed effort on goal by Papiss Cisse from inside the penalty box misses to the right of the goal.
Free kick awarded for a foul by Vurnon Anita on Wesley Hoolahan. Free kick crossed by Javier Garrido, Papiss Cisse makes a clearance.
James Perch challenges Robert Snodgrass unfairly and gives away a free kick. Free kick crossed left-footed by Andrew Surman.
Inswinging corner taken by Yohan Cabaye, Mike Williamson takes a shot. Save made by John Ruddy.
A cross is delivered by Vurnon Anita.
Foul by Michael Turner on Demba Ba, free kick awarded. Yohan Cabaye crosses the ball from the free kick right-footed from right channel, Bradley Johnson makes a clearance.
Papiss Cisse takes a shot. Save by John Ruddy.
Andrew Surman delivers the ball, clearance by Steven Taylor.
The ball is sent over by Robert Snodgrass, clearance made by Steven Taylor.
Wesley Hoolahan has an effort at goal from outside the penalty area missing to the wide left of the goal.
Russell Martin fouled by Papiss Cisse, the ref awards a free kick. Russell Martin takes the direct free kick.
The ball is swung over by Hatem Ben Arfa, clearance made by Russell Martin. Yohan Cabaye has an effort at goal from just outside the box which goes wide of the right-hand post.
Corner from the right by-line taken by Yohan Cabaye, Close range header by Steven Taylor goes wide of the left-hand post.
Hatem Ben Arfa takes a shot. Save by John Ruddy.
The referee gives a free kick against Steve Morison for handball. Hatem Ben Arfa takes the free kick.
Robert Snodgrass has an effort at goal from just inside the box that misses to the right of the goal. Corner taken by Robert Snodgrass from the right by-line, Steve Morison takes a shot. Andrew Surman takes a shot. Free kick awarded for an unfair challenge on Bradley Johnson by Yohan Cabaye. Free kick taken by John Ruddy.
Bradley Johnson challenges Demba Ba unfairly and gives away a free kick. Centre by Yohan Cabaye, Headed effort on goal by Mike Williamson from inside the penalty box misses to the right of the target.
Andrew Surman takes a shot. Steve Harper makes a save.
The ball is sent over by Jonas Gutierrez, Michael Turner manages to make a clearance.
The game restarts for the second half.
45:00 +2:26 Half time
Half Time The first half comes to an end.
Steve Morison concedes a free kick for a foul on Steven Taylor. Free kick taken by Steven Taylor.
Penalty taken by Papiss Cisse and missed.
Steve Morison gives away a Penalty for an unfair challenge on Mike Williamson.
Vurnon Anita fouled by Andrew Surman, the ref awards a free kick. Free kick crossed right-footed by Yohan Cabaye from right channel.
Andrew Surman gives away a free kick for an unfair challenge on Vurnon Anita. Free kick taken by Steve Harper.
The ball is delivered by Yohan Cabaye.
Bradley Johnson fouled by Davide Santon, the ref awards a free kick. John Ruddy restarts play with the free kick.
Inswinging corner taken by Robert Snodgrass from the right by-line.
Russell Martin delivers the ball, blocked by Steven Taylor.
Demba Ba concedes a free kick for a foul on Leon Barnett. Michael Turner restarts play with the free kick.
The ball is crossed by Robert Snodgrass, save made by Steve Harper.
Shot by Papiss Cisse from just outside the area goes over the net.
Free kick awarded for an unfair challenge on Steve Morison by James Perch. The free kick is delivered left-footed by Robert Snodgrass from right channel, Michael Turner concedes a free kick for a foul on Mike Williamson. Direct free kick taken by Steve Harper.
Davide Santon produces a cross, Effort from the edge of the area by Yohan Cabaye goes wide of the left-hand upright.
The ball is sent over by Vurnon Anita, clearance by Jonathan Howson.
Effort from deep inside the area by Yohan Cabaye misses to the left of the target.
Corner taken right-footed by Yohan Cabaye from the left by-line, clearance by Leon Barnett.
Vurnon Anita produces a cross, clearance by Leon Barnett.
Free kick awarded for an unfair challenge on Davide Santon by Robert Snodgrass. Steven Taylor takes the free kick.
The ball is swung over by Wesley Hoolahan, Davide Santon makes a clearance. The ball is swung over by Wesley Hoolahan, Robert Snodgrass takes a shot. Mike Williamson manages to make a clearance. Free kick awarded for an unfair challenge on James Perch by Wesley Hoolahan. Free kick crossed right-footed by Yohan Cabaye.
The ball is crossed by Hatem Ben Arfa, Bradley Johnson makes a clearance.
The official flags Davide Santon offside. John Ruddy takes the indirect free kick.
Mike Williamson fouled by Steve Morison, the ref awards a free kick. Free kick taken by Steve Harper.
The referee blows for offside. Indirect free kick taken by Leon Barnett.
Yohan Cabaye produces a right-footed shot from just outside the box that goes wide left of the goal.
Assist by Hatem Ben Arfa.
18:55 Goal scored
Goal! - Demba Ba - Newcastle 1 - 0 Norwich Demba Ba finds the net with a goal from deep inside the penalty box low into the middle of the goal. Newcastle 1-0 Norwich.
Steve Morison challenges Vurnon Anita unfairly and gives away a free kick. Yohan Cabaye delivers the ball, James Perch takes a shot. Leon Barnett gets a block in.
Vurnon Anita sends in a cross, Jonathan Howson gets a block in.
Davide Santon fouled by Bradley Johnson, the ref awards a free kick. Direct free kick taken by Steve Harper.
Unfair challenge on Russell Martin by Jonas Gutierrez results in a free kick. Robert Snodgrass delivers the ball from the free kick left-footed from right wing, clearance made by Papiss Cisse.
Steve Morison delivers the ball, clearance by Mike Williamson.
The ball is delivered by Bradley Johnson, save by Steve Harper.
Corner taken by Andrew Surman from the left by-line played to the near post, Jonas Gutierrez makes a clearance.
The ball is swung over by Javier Garrido, clearance made by Mike Williamson.
Centre by Robert Snodgrass, Mike Williamson makes a clearance.
Jonas Gutierrez produces a cross, Bradley Johnson makes a clearance.
The ball is swung over by James Perch, blocked by Andrew Surman.
John Ruddy restarts play with the free kick.
Substitution Michael Turner is brought on as a substitute for Sebastien Bassong.
Demba Ba is ruled offside.
Javier Garrido sends in a cross, Wesley Hoolahan takes a shot. Mike Williamson gets a block in. Corner taken by Andrew Surman from the left by-line. Wesley Hoolahan gives away a free kick for an unfair challenge on Hatem Ben Arfa. Free kick taken by Steve Harper.
The ball is crossed by Davide Santon, clearance made by Sebastien Bassong.
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