Mikel Arteta's side were bidding for a fourth successive league win but could find no way through an obdurate Palace who, if anything, might feel they could have emerged with a win.
Arsenal controlled the second half but rarely troubled Palace goalkeeper Vicente Guaita.
They remained in 11th spot in the standings with 24 points from 18 games with Palace two places lower with 23 points.
With the locked down capital reeling under the COVID-19 surge, this was perhaps a good night for fans to have no other option but to watch the game on television.
Incessant drizzle all day created the perfect, zippy playing surface, but rather than inspire a feast of attacking play it was a cagey affair as Palace stretched their unbeaten league run against Arsenal to five.
The main positives for Arsenal were a first home clean sheet in the league this season and the return of Thomas Partey as a second-half substitute having recovered from injury.
Palace manager Roy Hodgson was happy with a point.
"I am more than satisfied. We created opportunities and in the second half we wasted positions on the break. We defended excellently and I am very proud of them," he said.
Eze released Benteke in on goal but his shot was tame and it was Eze's free kick which Tomkins headed against the crossbar.
Lacazette did fire one chance into the side-netting but all in all it was a laboured display by Arteta's side.
"We probably didn't do enough to win the game," Arteta said. "We are playing a lot of games and you can see fatigue is paying a price, many players aren't fresh."