Chelsea winger Pedro was sent off after catching Mohamed Elneny with a tackle from behind and Arsenal equalised from the resulting free-kick, Sead Kolasinac converting a free header from Xhaka's pass.
It took just a matter of seconds for Moses to break the deadlock after the start of the second half.
While Chelsea's starting XI was closer to its top unit than Arsenal, Blues coach Antonio Conte showed how much he cared about the match by letting goalkeeper Thibaut Courtois take a penalty.
Former Liverpool captain Steven Gerrard was critical of the system, and said: "I liked the format that we already had". On came another of Arsenal's summer signings, Kolasinac. Both sides met in the final of the Champions League where Arsenal ran out winners.
"It is great sportsmanship from him", Mertesacker told Arsenal Player of Cahill's apology.
Batshuayi and Morata are expected to compete for one starting spot as the central striker in Antonio Conte's 3-4-3 formation this season, but the Belgium worldwide dismissed any suggestion that he revelled in his rival's disappointment on Sunday.
Created to prevent a perceived advantage to the team going first, the system sees team A take the first kick followed by team B - before team B go again.
Arsenal were good value for their win, having dominated the majority of the game with Chelsea looking a bit off color just six days ahead of the start of their Premier League title defense.
Alexandre Lacazette was handed a starting berth by manager Arsene Wenger for today's Community Shield showdown with Chelsea at Wembley.
"We put ourselves in a hard position just after half-time, but in the end we produced a performance that we did at the end of last season", the Frenchman said.
Sven Ulreich saved two penalties Saturday as Bayern Munich defeated Borussia Dortmund 5-4 in a shootout to win the season-opening German Supercup.