Girgensons erased a 1-0 deficit with a second-period goal and the score remained knotted until the shootout.
Girgensons, however, beat Ottawa's Robin Lehner in the 10th with a backhander and Sabres goalie Ryan Miller then stopped Erik Condra to secure the victory.
Miller stopped 35 shots as Buffalo logged just its second win in 10 games.
Michalek scored in regulation and Lehner finished with 35 saves for the Senators.
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