Boyle capitalised on a goalkeeping error midway through the first half to give Hibs the lead, before Daniel Mackay doubled the advantage in the 69th minute.
Nicolas Pepe missed a penalty three minutes later, before Emile Smith Rowe scored a late consolation, as Hibernian held on to win its first meeting with the Gunners since 1955.
Mikel Arteta was disappointed to come away from Easter Road with the defeat, saying:
"I'm always disappointed when we lose a football match but it is the first game, we played with many kids and we only had four training sessions," Arteta said.
"We've trained really hard and you could see that the players were a little bit leggy.
Arsenal remains in Scotland for another pre-season friendly, taking on Glasgow giant Rangers on Sunday (AEST).