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.
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.
While Stoke's defenders ball-watched, Squillaci ran in to head home from close range.
However, Arsenal's defence held firm and Stoke were beaten away for the fifth successive league match leaving them 10th in the table.
