Alexis Sanchez celebrates after his header was diverted into the Palace goal by Damien Delaney
The 26-year-old made his first start of the season after just two weeks of pre-season training.
Sanchez missed several chances to get his name on the scoresheet in the first half but with the score at one apiece, he rose highest to meet Hector Bellerin's right wing cross which was diverted into the net for an own goal by Damien Delaney.
Wenger told BBC Sport: "That was a bit scary when we missed those chances. We are used in our game to be punished after that which makes the three points more important.
"Alexis Sanchez has had only two weeks' training but he still had the mental resources to score a vital goal for us.
"It's not a 100 per cent fit Sanchez but it's a 100 per cent motivated Sanchez and sometimes that's enough."
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