The Gunners made it hard on themselves by allowing James Tomkins to score Palace's second with a minute remaining in normal time.
But out of nowhere, after 50 minutes, Roy Hodgson's men had their equaliser through Andros Townsend, who scored with Palace's first shot on target for the game.
It looked like another lowly away night for Arsenal before Alexis Sanchez stepped up to fire home two goals within four minutes to ease the pressure. The second goal was set up through a sublime pass by Jack Wilshere, who made his third straight Premier League start for the Gunners.
Tomkins late goal was a display of Palace's determination, which was duly recognised by the Eagles faithful who gave the players a standing ovation after the final whistle.
Speaking after the game, Wenger was pleased with his side's performance.
"Overall it was a convincing win even though in the second half it was harder than the first," said the Frenchman.
"We found the resources to score two great goals and from then we never gave up.
"You want to win the game no matter how you suffer in the end. We did that.
"We gained composure. We have come here and it is a difficult game for everyone in the league. We suffered a bit but for the biggest part of the game we played well."