Blue Jays pitcher J.A. Happ did his best to match Darvish, striking out eight over six innings and retiring the first nine batters he faced in the match to equal a Toronto record.
"That's as good a three innings as you're going to see anywhere," Toronto skipper John Farrell told reporters.
Craig Gentry's groundout to second put Texas on the board in the fifth but Toronto scored one of their own in the bottom of the inning when Rajai Davis singled to centre.
The Rangers added another in the seventh but the Blue Jays grounded out the win.
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