The Spaniard stroked in a 47th-minute penalty to give the Gunners the lead after Serge Gnabry was fouled by Adlene Guedioura, but was then dismissed for bringing down Marouane Chamakh as the last man.
But Wojciech Szczesny made several superb saves to prevent Palace finding an equaliser, and Olivier Giroud headed in Aaron Ramsey's scooped cross to seal the win late on.
|VIEW FROM SELHURST PARK
|By Ewan Roberts
Arsenal remain at the top of the table, though Crystal Palace can claim a moral victory. The Eagles defended brilliantly, undone by a rash penalty and a late Olivier Giroud header.
When Mikel Arteta was dismissed, the momentum of the game shifted and the south Londoners grew in confidence. But for the brilliance of Wojciech Szczesny, who did brilliantly to deny both Joel Ward and Mile Jedinak, the Eagles would surely have claimed at least a point.
As it is, the Gunners continue to show their new-found reserves of spirit and resolve, while Palace can take heart from a committed performance that suggests they aren't dead and buried just yet.
Arsenal created their first chance after just three minutes when Giroud headed Bacary Sagna's right-wing cross just over the crossbar.
The visitors were forced to change things inside the first 10 minutes, though, Flamini replaced by Gnabry after he limped off with an apparent groin injury.
Palace competed well for large periods of the first half, and had opportunities to take the lead themselves, Bannan heading over before Chamakh tested Szczesny with a long-range effort.
Both sides continued to trade chances in an open game, although Arsenal were aggrieved not to have been awarded a penalty as Chris Foy ruled that Damien Delaney's foul on Gnabry had been outside of the box.
But Foy did point to the spot when Gnabry was brought down by Guedioura less than two minutes into the second half, enabling Arteta to step up and fire home confidently from 12 yards.
Wenger's men began to dictate proceedings following the opener and should have doubled their advantage shortly after, Giroud missing the target from point-blank range after good work down the right from Sagna.
However, the game was completely changed after 65 minutes when goalscorer Arteta was shown a straight red card for pulling down Chamakh as the Moroccan attempted to break through on goal.
Palace immediately began to take charge following Arteta's dismissal, Szczesny performing heroics to tip Joel Ward's fierce effort onto the crossbar before producing another flying save to keep out Mile Jedinak's volley.
But Giroud wrapped things up three minutes from time to end the hosts' hopes of a late leveller.