Lukas Podolski, Santi Cazorla and Olivier Giroud all made their debuts but none of the new attacking trio could get on the scoresheet as Arsene Wenger's team failed to lift the gloom following van Persie's £24 million move to Manchester United earlier in the week.
Giroud came off the bench and missed Arsenal's best chance of the day when he was sent through on goal, but Germany striker Podolski found chances difficult to come by.
Aside from van Persie, Wenger was also without Cameroon midfielder Alex Song, who has moved to Barcelona.
It meant Abou Diaby and Mikel Arteta were protecting a defence missing Laurent Koscielny with a calf problem.
Spanish winger Cazorla was in the starting line-up following his move from Malaga and Podolski also made his first appearance for the club.
But it was Sunderland who made the first decent chances of the game.
Stephane Sessegnon was up front on his own but he offered a warning of his threat when he skipped down the right and put in a good cross.
Then he set up James McClean by sliding a pass behind the Arsenal defence and it needed Wojciech Szczesny to use his feet to make a sharp save.
Jack Colback was the next to get a sight of goal. Sessegnon created the chance again with a well-weighted pass but Coback's shot was just too close to Szczesny.
Cazorla was the heart of Arsenal's best early chances, starting with a drive turned over the crossbar by Simon Mignolet.
He also shot just wide after an exciting run from Gervinho saw the Ivory Coast winger trick Craig Gardner before cutting the ball back.
Podolski got his first chance midway through the first half when Carl Jenkinson's cross caused confusion in the Sunderland penalty area, but the visitors scrambled away before the striker could get a shot away.
Diaby got closer with Arsenal's next attack, after Podolski fed him the ball 30 yards from goal.
His shot was angled towards the bottom corner and Mignolet was required to tip it around the post.
Before the end of the first half, Craig Gardner pulled off a last-ditch tackle to deny Podolski and Coback hit the side netting at the other end.
In the second half, Kieran Richardson was booked for ending a promising Arsenal attack with a cynical challenge but Podolski fired the free-kick over the crossbar.
Cazorla got closer when he flashed a volley just wide of the post from a similar distance.
Theo Walcott also fired into the side netting as Sunderland clung onto their clean sheet.
Wenger decided to send on Giroud for his debut in place of Podolski, while Louis Saha was also brought on for Sessegnon as Sunderland boss Martin O'Neill looked to snatch the win.
Giroud had a sight of goal when Sunderland lost the ball on the edge of the area, but he crossed when he should have shot and the chance was gone.
Before the end, Cazorla sent Giroud through on goal but the France striker fired wide with just Mignolet to beat.
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