Both African stars were on target for their teams at the Emirates Stadium but Zaha's effort was crucial in securing maximum points for Roy Hodgson's side in north London.
Christian Benteke broke the deadlock in the 17th minute after converting Luka Milivojevic's free-kick with a header.
Three minutes into the second half, Mesut Ozil drew Unai Emery's side level but Zaha restored Crystal Palace's lead in the 61st minute, courtesy of an assist from Benteke which was then followed by James McArthur's header in the 69th minute.
Following a nice run through the flanks, Aubameyang reduced the deficit for the Gunners by driving his low shot past goalkeeper Vicente Guaita in the 77th minute to register his 19th league effort of the season.
Nigeria's Alex Iwobi was introduced in the 46th minute and his contribution was crucial to Arsenal's resurgent display in the second half.
Despite the defeat, Arsenal remain fourth in the Premier League table with 66 points from 34 matches while Palace climbed to 12th in the log with 42 points from 35 games.
Later in June, Zaha's Cote d'Ivoire will join 23 teams at the 2019 Africa Cup of Nations while Aubameyang's Gabon failed to qualify for the continent's foremost football competition.