Jesse Joensuu also scored for the Oilers (4-1-1), who did not dress many of their top offensive threats.
Chris Thorburn replied for the Jets (1-3-2), who have lost three straight in exhibition play.
It took a while for either team to get on the board in a penalty-filled first period. The Jets finally started the scoring with just under a minute remaining as a Thorburn shot that appeared to be going wide hit the stick of Oilers starter Devan Dubnyk and deflected into the net.
Edmonton tied the game just under three minutes into the second period when Tyler Pitlick put the puck in front of the net for a hard-charging Joensuu to direct past Jets goalie Edward Pasquale. It was Joensuu's third goal of the pre-season.
The Oilers went up 2-1 midway through the second period, when Acton deflected an Anton Belov point shot through Pasquale's legs.
Dubnyk made up for his gaffe earlier in the game with a five-alarm glove save on Olli Jokinen late in the second on a Winnipeg power play.
There was no scoring in the third period.
Notes: It was the second pre-season meeting between the two teams. The Jets won the first match-up 3-2 on Sept. 18. ... The Jets were making their first visit to Rexall Place since March 1996. The Oilers and Jets will face off to start the regular season on Oct. 1 in Edmonton. ... After being roughed up in their last game against the Vancouver Canucks, resulting in a broken jaw and several missing teeth to centre Sam Gagner, the Oilers added some toughness in the form of Steve McIntyre on Monday. McIntyre, who will be joining the Oil for the third time in his career, was picked up off of waivers from Pittsburgh. ... Hulking six-foot-five centre prospect Adam Lowry played in his first game of the pre-season for Winnipeg since hurting his neck in the first scrimmage of camp.