Alexis Sanchez tapped in Mesut Ozil’s square pass to the relief of those inside a sparsely populated Emirates Stadium.
As Arsenal increased in urgency, Sanchez bundled in Olivier Giroud’s cut-back to renew their hopes of a top-four finish for a 21st successive season.
The Gunners are a point behind fourth-placed Liverpool ahead of Sunday’s final matches.
Arsene Wenger’s men must beat seventh-placed Everton and hope the Reds slip up against already relegated Middlesbrough at Anfield.
Patience pays off for Arsenal
Arsenal started the evening needing to win – and preferably by a big margin – if they were to realistically sneak into the top four.
The Gunners knew defeat against rock-bottom Sunderland, who had managed just three away wins all season, would end their hopes if Manchester City earned a win against the Baggies.
And with City cruising to a 3-1 win in their game, even a draw would have left Arsenal struggling.
Until Sanchez’s intervention, it looked as though Wenger’s side would be left frustrated by a lack of conviction in front of goal and some stubborn Sunderland defending.
Finally the Gunners found their breakthrough with 20 minutes left. Granit Xhaka picked out Ozil with a clever chip over the Sunderland defence which was put back across goal by the German for Sanchez to tap in.
Arsenal knew just a draw against Everton might be enough to catch Liverpool if they wiped out the Reds’ superior goal difference, and Wenger urged his side to push for more goals from the touchline.
Sanchez was lurking in the six-yard box at the right time again to convert Giroud’s volleyed pass but, although Shkodran Mustafi hit the woodwork, Arsenal could not add to their tally.
Ultimately patience paid off for the Gunners, who are now hoping Middlesbrough can do his team a favour at Anfield.
“Sunderland did fight and that’s what you want from every team,” said Wenger afterwards.
