Sebastien Squillaci, who was playing in place of the injured Laurent Koscielny, was the unlikely match-winner when he headed home his first Premier League goal after only eight minutes.
However, Fabregas went off with a hamstring injury after 15 minutes and Walcott was stretchered off with a damaged ankle 20 minutes from time and will miss Sunday's Carling Cup final against Birmingham City at Wembley.
Arsenal manager Arsene Wenger told reporters: "Theo Walcott has an ankle sprain and he is out. For how long, I don't know, but he is definitely out of Sunday.
"Fabregas has a hamstring problem. We will assess that tomorrow. It is impossible to see how serious it is tonight. We will know tomorrow." With Arsenal chasing four trophies in the Premier League, League Cup, Champions League and FA Cup, Wenger will be concerned about a lengthening injury list.
Dutch winger Robin Van Persie and Koscielny are already doubtful for Wembley, and although Fabregas went off as a precautionary step, he will be desperate to play against Barcelona in the Champions League at the Nou Camp on March 8.
Walcott's woes looked more serious after he was carried off the Emirates Stadium pitch following a challenge from Stoke's Dean Whitehead. As he fell, his left ankle caught and twisted in the turf and he looked to be in some pain.
The three points left Arsenal with 56 points from 27 games, while United are on 57 with a game in hand. Manchester City are a distant third with 49 points from their 27 games.
United were in action in France on Wednesday, drawing 0-0 with Olympique Marseille in their Champions League last-16 first leg match.
Arsenal asserted their dominance early in the game when Walcott hit the post in the opening minutes before Squillaci, guilty of some erratic performances this season, scored after a cross from Nicklas Bendtner following a Jack Wilshere corner.
While Stoke's defenders ball-watched, Squillaci ran in to head home from close range.
After Fabregas went off, Arsenal appeared to lose some cohesion and Stoke went close to an equaliser with John Carew, Jermaine Pennant, Ryan Shawcross and Robert Huth all having good chances to score.
However, Arsenal's defence held firm and Stoke were beaten away for the fifth successive league match leaving them 10th in the table.
