Toronto took control with five runs in the third off Mike Pelfrey (5-11) and survived down the stretch to win for the sixth time in eight games.
Lawrie eventually delivered a two-out single that drove in two runs and Sierra followed with a double for two more.
R.A. Dickey (12-12) went 6 1/3 innings for the win, giving up three runs on seven hits.
Minnesota scored four times over the last three innings, but came up short. Chris Colabello hit a two-run homer in the seventh, the Twins added a run in the eighth but left the bases loaded and Josmil Pinto hit a leadoff homer in the ninth off Casey Janssen.
Janssen then survived an infield error later in the inning to pick up his 28th save.
Swim Week Miami Beach 2014 [PHOTOS]