Jackson (3-3) allowed a pair of runs, working around three walks while striking out three for the Nationals, who won their fourth straight to open a three-game series at Rogers Center.
Blue Jays starter Brandon Morrow (7-4) faced only one batter before exiting with an injury but still sustained the loss. The right-hander strained an oblique muscle after walking Steve Lombardozzi to open the game.
Chad Beck relieved and gave up three runs (two earned) over the next 3 2/3 frames.
Yan Gomes belted a two-run homer and Colby Rasmus added solo shot for Toronto.