Bautista helped Toronto strike first with a three-run homer in the first inning and Lawrie padded the cushion with a two-run blast in the sixth. Bautista had three hits and Juan Francisco drove in a pair of runs for the Jays, who had dropped the previous three games in this set.
Mark Buehrle (7-1), who entered as the AL leader with a 1.91 ERA, survived six hits and five walks to allow just a pair of runs in six-plus innings.
C.J. Cron homered for the Angels, who came up short of completing their first four-game sweep ever in Toronto. C.J. Wilson (4-3) struck out eight but yielded five runs on six hits to absorb the loss.
Steve Tolleson started the home half of the first with an infield single and Melky Cabrera walked. Bautista then stepped up and crushed a 2-1 offering well over the wall in left field, providing Buehrle with an early 3-0 lead.
The Angels got two of those runs back in the third inning, when Collin Cowgill walked and Grant Green singled for Mike Trout, who plated both runners when he ripped a two-out double to the wall in center.
But Lawrie's two-run shot in the sixth made it 5-2 and provided Toronto's bullpen all the insurance it would need.
Green and Erick Aybar singled to start the seventh, and Buehrle exited with two on and no outs in favor of Steve Delabar. Trout struck out and Albert Pujols grounded into a double-play, ending the threat.
Delabar allowed just the one run in two innings and Casey Janssen worked a scoreless ninth to secure the victory.