Arsenal boss Arsene Wenger admits their title chances were over if they had failed to beat Wolves.
Denmark striker Nicklas Bendtner came off the bench to head a crucial goal which keeps the Gunners in touch as the race for Barclays Premier League supremacy enters a thrilling conclusion.
Wolves defended bravely and looked to have overcome the sending-off of captain Karl Henry for a rash challenge on Tomas Rosicky before Bendtner's late, late intervention sent the home crowd into delirium.
"It keeps us in the title race, yes. If we had not won, it would have been finished," said Wenger.
"You know if you are five points behind Chelsea with five games to go, you can forget it, but with three points it is feasible.
"We have a difficult programme but they have a difficult programme as well."
Wenger continued: "It was important to forget Barcelona for 24 hours and focus on today's game, and that was not easy. But we did it well - I think we had a good focus.
"We were a bit jaded physically, but we kept going and we were serious, we didn't make a mistake at the back.
"In the end we got a deserved victory against a resilient Wolves team who had a great goalkeeper.
"We kept it late, as with many times, but overall we deserved to win the game."