United manager Erik ten Hag was left shaking his head in frustration.
The game swung from end to end over a final tense few minutes, with Onana leaping to push away shots from Arsenal substitute Gabriel Martinelli and Declan Rice.
United, who were hoping to bounce back after a woeful 4-0 loss at Crystal Palace on Monday, are eighth with two games left. They trail sixth-placed Newcastle by three points in their quest for a European berth next season, setting up a key showdown when the Magpies visit Old Trafford on Wednesday.
Trossard's goal was the 82nd Ten Hag's team have conceded this season in all competitions -- their most in a single campaign since 1970-71
United enjoyed plenty of the ball in the final third, and had 14 shots to Arsenal's 11, but struggled to create many quality chances.
Alejandro Garnacho was United's biggest threat, particularly in the second half. He launched one shot wide and sent another into the side netting before hanging his head in frustration.
The visiting fans, whose singing did not let up all evening, erupted at the final whistle after a game that was tighter than predicted. Not even the torrential downpour could dampen their celebration after the job done by Mikel Arteta's team.
Arsenal host Everton in their season finale, while City are at home to West Ham United.
Published 12 May 2024, 18:05 IST