Man-of-the-match Robin van Persie scored twice and a first senior goal by Ivory Coast international Emmanuel Eboue broke down the stubborn resistance of the home side.
The Gunners' strength in depth proved too much after a goalless first half and once the deadlock was broken just after the hour, the outcome was never in doubt.
Sunderland made six changes to the side beaten in Sunday's North East derby at St James' Park, while Arsenal manager Arsene Wenger almost made a clean sweep to last weekend's winning team, only central defender Pascal Cygan surviving.
But there was still enough experience in the Gunners side, including the return from injury of Sol Campbell and the inclusion of van Persie and Philippe Senderos.
The kick-off was delayed 15 minutes due to crowd congestion, the attendance was just short of the 48,000 capacity, and Arsenal quickly took the game by the scruff of the neck.
But they created few clear-cut chances despite enjoying the bulk of possession and failed to seriously test rookie goalkeeper Ben Alnwick, with Sunderland faring no better at the other end.
Casual play in the home defence, Danny Collins slipping and losing possession allowing Arturo Lupoli to break clear, but Nyron Nosworthy came to the rescue with a timely interception.
Alnwick punched out a free-kick from the lively van Persie but when Steve Caldwell was penalised for a challenge on Fabrice Muamba, the Dutchman wasted a glorious chance by blazing the free-kick over the bar.
After van Persie had forced the first corner in 22 minutes, Alnwick again denying the Arsenal striker by diving to his right to keep out a low drive, the Gunners continued to have the better of the exchanges.
Sunderland's response was weak efforts from Jonathan Stead and Andy Welsh with the visitors' attacks always posing more threat without being to apply the killer finish.
But they should have gone ahead just before the break when Senderos was left completely unmarked at the far post from a left-wing corner only for the Swiss defender to head wide.
Sunderland lost the injured Collins three minutes into the second half and almost immediately had Alnwick to thank for denying van Persie with a brilliant stop from close range.
But Arsenal finally found a way through with the breakthrough in the 61st minute, quickly followed by a fiercely struck penalty kick to completely knock the stuffing out of the plucky home side.
The quick-footed Quincy Owusu-Abeyie found Alexandra Song who played the ball into the path of Eboue for the Ivory Coast international to hit a fierce 20-yard drive into the net.
Five minutes later substitute Dan Smith and Justin Hoyte combined to bring down Lupoli and there was no messing about with the spot-kick, van Persie driving the ball just inside the upright.
The elegant van Persie piled on the agony for the home fans in the 87th minute after being released by Sebastian Larsson, slipping the ball past Alnwick to complete a comfortable win.