The midfielder had volleyed the Gunners - now level with leaders Chelsea, although having played a match more - in front, before being taken off as a precaution.
Burnley - who had picked up just one point away all season - equalised at the start of the second half through David Nugent, before a fine finish from England forward Walcott and Andrey Arshavin's stoppage-time strike sealed victory.
The events of last weekend at Stoke were still on the minds of Arsenal fans as they chanted Aaron Ramsey's name before kick-off, while a large banner was also displayed in support of the promising Wales international and the players wore 'Get Well Soon Aaron' T-shirts during the warm-up.
Arsenal started brightly, with a last-gasp tackle from Tyrone Mears denying Nicklas Bendtner in the six-yard box before Thomas Rosicky fired a 20-yard effort over.
At the other end, Clarke Carlisle headed a corner straight at Manuel Almunia.
Walcott - who came in for some criticism after his midweek outing for England - looked lively down the right, but lacked a decent final delivery.
On 13 minutes, Emmanuel Eboue and Fabregas played a neat one-two which released the Arsenal captain into the right side of the penalty area, but his low shot dragged wide.
Daniel Fox relieved the pressure when he fired in a 25-yard effort, but Almunia collected it comfortably.
Arsenal appealed for a penalty when Walcott went down under a shoulder charge from Mears, but referee Chris Foy was not interested.
There was a stoppage when Samir Nasri and Burnley goalkeeper Brian Jensen collided going for a 50/50 ball.
Bendtner almost got on the end of Eboue's low cross through the Burnley box as the one-way traffic continued.
Arsenal took the lead on 35 minutes through a superbly-crafted effort.
Nasri made space for himself on the edge of the Burnley box, before chipping the ball over the defence.
It had the perfect weight for Fabregas to get ahead of Alexander and volley through Jensen's legs for his 17th goal of the season.
Bendtner then fired wide when sliding into the six-yard box as the Gunners looked for a quick-fire second.
Walcott squared up to Fox after the Burnley midfielder slid in for a 50/50 ball on the touchline, before calm was restored after a talking to by the referee.
Fabregas, who had not been running freely for some time, was then replaced by Diaby.
Arsenal came out in determined mood for the start of the second half.
Walcott whipped over a fine cross from the right, which Bendtner - who had scored a good header at Stoke - somehow glanced wide from six yards out.
The Dane was not having a good afternoon, as he then blazed over after Walcott had cut the ball back from the goal-line following Gael Clichy's deep centre.
Walcott then had a go himself after being released by Nasri, but his angled 20-yard drive flew just over.
Arsenal were made to pay when Burnley equalised on 50 minutes.
A clearance from Eboue was headed back towards the penalty area by Leon Cort, and as the defence hesitated, the ball bounced right through to Nugent, who lifted it past Almunia.
Arsenal suddenly had more urgency, but were now faced with a determined 10-man rearguard.
Walcott was away again down the right, and his shot was parried behind by Jensen.
The England forward finally had his goal on the hour after cutting inside and stroking a low, left-foot effort inside the far post.
Arshavin came on for Rosicky as Arsenal looked to up the tempo.
The Russian, though, blazed over after more industrious work from Walcott.
Bendtner once more stroked the ball wide from six yards out when it looked a certain goal after Walcott's low centre.
The hapless Dane's afternoon was eventually ended when he was replaced by Eduardo with 17 minutes left - the striker being given a somewhat ironic standing ovation.
To their credit, Burnley continued to look for an equaliser, and substitute Steven Thompson fired over with five minutes left.
Arsenal finished strongly, though, as Jensen pushed Walcott's curling effort behind before Arshavin stroked in a third during stoppage time.