First-half goals from Santi Cazorla and Olivier Giroud gave Wenger's men a platform at Selhurst Park, but the visitors were then penned back for long spells by Alan Pardew's men.
Substitute Glenn Murray gave the hosts hope when he pulled one back late on and he could have single-handedly gained Palace a point when his header struck the post deep into stoppage time.
Wenger acknowledged his side were fortunate not to squander their lead, adding that several of his players switched off too early.
"Crystal Palace is a team who play with a big intensity and a very direct game and for us, it was important to resist and try to play," he told his post-match media conference.
"We did that well but at 2-0 in the second half we tried much more to come out and protect our advantage, [rather] than continue to play and put them under pressure.
"We missed goal number three and when they came back to 2-1 we were a bit lucky, a bit fortunate, but overall we did fight and it was a very important win for us.
"Certainly they [Arsenal's players] thought it was done and we know in the Premier League it is never done, especially at 2-0. With that ball on the post, we were a bit fortunate."
'Obviously Messi is the best player in history and being compared to him means that you're doing things right, but I try to be myself': Barcelona star responds to comparisons with Argentine legend
'Darwin Nunez would be gold for Arsenal': Liverpool legend claims Gunners should have signed Uruguayan striker in January
