Vela scored in the third minute when Theo Walcott passed the ball into the six-yard box and the Mexico international slid in to tap past Celtic goalkeeper Lukasz Zaluska.
Sagna scored with less than a minute to go before halftime with a left-foot volley after a casual pass from Tomas Rosicky found him on the edge of the area.
Nasri scored in the 51st from close range after Walcott set him up inside the area.
Celtic, quiet for most of the match, staged a late rally by pulling a goal back in the 73rd when Daryl Murphy slotted the ball past Arsenal goalkeeper Manuel Almunia. Ki Sung-Yueng put Celtic within a goal of Arsenal in the 82nd, scoring from close range off a low cross from the right.
Celtic was also awarded a penalty in the 68th after Jack Wilshere pulled down Marc-Antoine Fortune but Georgios Samaras fired the ball well wide of goal.
The Scottish team's only other clear chance before that came from a free kick a few minutes after the first goal, but Almunia dived to his right to catch the ball.
In the early match, Lyon's Jimmy Briand scored a late equalizer to secure a 1-1 draw against AC Milan.
Lyon, Champions League semifinalists last season, dominated the game but failed to take its chances. The French side fell behind when Milan's Marco Borriello opened the scoring in the 55th.
Briand equalized when he converted a cross from Miralem Pjanic with 10 minutes remaining.
On Saturday, Celtic rallied to a 2-2 draw with Lyon and Arsenal drew 1-1 with AC Milan.
Arsenal manager Arsene Wenger used 18-year-olds Wilshere and Emmanuel Frimpong in midfield for a second straight day after impressing Saturday.
Wilshere played in central midfield and was involved in Arsenal's first goal Sunday, passing from the edge of the area to Walcott, who set up Vela. Wilshere nearly scored in the 35th when his fierce volley from the edge of the area rattled the crossbar. He followed up and his header was saved by Zaluska.
Frimpong, who is from Ghana, played in the holding midfield role and pushed several Celtic players off the ball to win back possession.
Questions still remain over the future of Arsenal's midfield star and captain, Cesc Fabregas. The Spain international returns to training on Thursday after appearing in the World Cup final on July 11.
Wenger reiterated that Fabregas will stay at Arsenal despite Barcelona's attempts to sign him, but urged his captain to commit publicly to the Gunners.
