Trailing 5-2 entering their final at-bat, Toronto struck for four runs off struggling Orioles closer Jim Johnson (2-5) to pull out the win in a stunning comeback.
After Brett Lawrie popped out, Anthony Gose drew a walk and Lind scored on Mark De Rosa's fielder's-choice grounder to make it 5-4.
That brought up Kawasaki, who belted a pitch into the left-center field gap that rolled to the wall, scoring Gose and De Rosa with the tying and winning runs.
Kawasaki finished 3-for-5 and also delivered an RBI single in the eighth for Toronto, which earned a split of its four-game series.
Steve Delabar (4-1) was credited with the decision despite allowing two runs in the top of the ninth.
Johnson was roughed up for his fourth blown save in six appearances for Baltimore.