Lind's clout in the first inning put the Blue Jays ahead to stay and Rasmus added his own two-run blast in the fourth, doubling the lead.
R.A. Dickey (6-8) notched the victory, working around seven hits and three walks to allow just one run over 5 2/3 innings. The knuckleballer struck out three as the Blue Jays reeled off a third consecutive win over Texas.
Rangers starter Josh Lindlom (0-2) was tagged for four runs on five hits over six innings.
Leonys Martin went 3-for-4 with an RBI for slumping Texas.