The Arsenal star's goal was the only thing that separated the two sides, although some may claim Arsene Wenger's outfit were never at full throttle.
Sunderland boss Roy Keane was furious at his side for taking their foot off the pedal down at the Reebok Stadium the previous weekend, but the Irishman could have no similar complaints this time around.
The Wearsiders had started brightly and any worries home fans had of a repeat of their side's lacklustre display away to Bolton Wanderers were quickly dismissed.
Keane rang the changes to his side, drafting in Marton Fulop in goal, while Dwight Yorke and Ross Wallace were given starting roles in the midfield engine room.
If Keane's intention had been to stir up his troops, it certainly had the desired affect, with Yorke and Wallace both causing the Gunners problems with lively first-half displays.
However, while the Black Cats showed plenty of promise in attack they couldn't find the final product early on.
Arsenal, while not at the fluent best, were also asking questions of the opposition defence and could have gone ahead on six minutes. Andy Reid lost possession in the middle of the park and the Gunners broke at pace.
Fulop, though, was equally quick and did well to save at the feet of Emmanuel Adebayor.
A minute later it was the hosts who were on the front foot, but Kenwyne Jones' header was comfortably saved by Lukasz Fabianski.
Seconds later Wallace went down to win a free-kick 25 yards out from goal, but Grant Leadbitter's effort went over the bar.
Yorke then tried his luck from distance on 15 minutes, but the shot was high, wide and handsome.
Then came a warning shot from Walcott as his long-range effort was saved by Fulop.
Before that Walcott had already shown brief glimpses of his blistering pace, but the Black Cats failed to heed any of the warning and paid the price on 24 minutes.
Brazilian midfielder Gilberto threaded through a pass and Walcott left Sunderland defender Danny Collins trailing in his wake, before sliding the ball under goalkeeper Fulop.
The hosts tried to find a way back into the game with Leadbitter going closest, but the midfielder headed over from the edge of the six-yard box.
Then with half-time looming the Wearsiders suffered a blow as they were temporarily reduced to ten men.
Jones, who had ploughed a lone furrow up front, left the field clutching his arm and didn't return after the break, being replaced by Roy O'Donovan.
That switch forced the red and whites to change their game plan and they eventually switched to two up front.
Both sides continued to press without really ever going for the jugular, but the Black Cats should have been on level terms on 74 minutes when O'Donovan fired wastefully wide.
The Irishman could have redeemed himself on 90 minutes, but a good save from Fabianski denied the hosts a way back into the clash.
However, even the defeat couldn't dampen the celebrations on Wearside as the fans treated the Sunderland squad to a rousing reception as they took to the field after the final whistle.
The Black Cats may have failed to halt the Gunners, but they lived to fight another Premier League day and that is all that mattered to red and whites among the full house.