Bobrovsky turned aside all 18 shots he faced before exiting early in the third period with an apparent lower-body injury while making a spectacular glove save on the Lightning's J.T. Brown.
He had to be helped off the ice and was replaced by McElhinney, who finishing with eight stops, including several during a Tampa Bay surge in the closing moments.
Nick Foligno got the game's only goal in the second period for the Blue Jackets, who were coming off a 3-1 loss to Boston Saturday.
Ben Bishop saved 20-of-21 shots for the Bolts.