Arsenal, seen as title contenders after their Community Shield victory over champions Chelsea two weeks ago, needed to bounce back from a shock home loss to West Ham United last weekend that cast doubts over their championship credentials.
“Alexis Sanchez has only had two weeks of training but still he had the mental resources to score us a vital goal today,” Wenger told reporters.
“We know it’s not a 100 percent fit Sanchez but a 100 percent motivated Sanchez and that at times can be enough.”
Making his first start for Arsenal this season despite not being fully match fit after helping Chile win the Copa America last month, Sanchez caused Palace problems from the start.
The Palace defence blocked three shots from Sanchez in the early stages, the first as he sought to tee up a chance rather than blast it at the first attempt, but it was only a matter of time before Arsenal opened the scoring.
Sanchez fed midfielder Mezut Ozil on the left, the German crossed low and France striker Olivier Giroud volleyed home a left-foot scissor kick in the 16th minute.
Arsenal could have been three goals up but were shocked when Palace defender Joel Ward scored a fine equaliser from the edge of the box in the 27th minute.
They were lucky Palace striker Connor Wickham’s effort two minutes after halftime hit Petr Cech’s post.
“It was a bit scary to look at the chances we missed,” Wenger said. “You thought we would be punished after that but we dug in and hung on in the last 10 minutes, and that too is important in the season.”
Wenger’s team, with Ozil so sharp that only one of his 55 passes failed to find a team mate, sealed the points in the 55th minute.
Sanchez rose above Ward to meet right back Hector Bellerin’s cross with a firm downward header which Damien Delaney tried to clear but only helped into the net.
“He (Sanchez) is direct, he runs at defenders, I knew he would come out on top in a one-to-one, he’s a fighter,” Wenger said.
(Editing by Ed Osmond)