Gary Roberts put Tampa Bay ahead just 1:24 into the first period but the Lightning were shut down the rest of the way by Lehtonen.
Stuart tied the score later in the first period and Koslov fired in the goal that turned out to be the game-winner early in the second. Kovalchuk's goal was an empty-netter with 10 seconds left to play.
Mike McKenna was credited with 21 saves for Tampa Bay.
Benedict Cumberbatch's dramatic reading of R. Kelly lyrics is just what you need
Beyonce flaunts bikini body, Blue Ivy in vacation pics