Ondrej Palat's late goal earned the Lightning a 3-2 series triumph.
Tampa Bay outshot the Rangers 51-29 to trim the series advantage to 2-1.
First period: Lightning outshot Rangers 15-12
Mika Zibanejad scored on a power-play one-timer 7:37 into the second. Zibanejad has six goals and 12 points in eight games.
Steven Stamkos scored a crucial bounce-back goal for the Lightning early in the third. Stamkos tied the game on Tampa Bay's 38th shot, a power-play one-timer, at 41:22.
Ondrej Palat's last-minute goal altered the outcome. Tampa Bay beat Igor Shesterkin 3-2 after Palat scored from close range.
Dylan Strome left the game when Ondrej Palat pushed him. Strome hobbled off the ice and into the locker room. Strome didn't return and is out for the series.