Barger's drive to right field off Justin Sterner (1-2) extended the Athletics' losing streak to six games. They have dropped 17 of 18 overall.
Toronto scored six times in the eighth, its second-biggest inning of the series. The Blue Jays scored eight runs in the second inning of a 12-0 blowout Thursday.
Vladimir Guerrero Jr. and Alejandro Kirk each had two hits and drove in a pair as the Blue Jays won their fifth straight and ninth in the past 13 games.
Swanson was making his first appearance of the season after being activated off the injured list before the game. He'd been sidelined since spring training because of a nerve issue in his arm.
Key stat
The A's have been swept in four of their past five series.
Up next
Blue Jays RHP Bowden Francis (2-6, 5.04 ERA) is scheduled to face Phillies RHP Zack Wheeler (6-2, 2.96) on Tuesday.
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