Ondrej Palat had two goals and an assist, and Tyler Johnson, Steven Stamkos and Alex Killorn each had one goal and an assist for the Lightning. They took a 2-1 lead in the best-of-7 series that continues Friday night at Amalie Arena.
The winner came about a minute after New York goalie Henrik Lundqvist made a terrific stop on J.T. Brown's breakaway.
Johnson, who paced Tampa Bay's 6-2 road victory in Game 2 with a hat trick, scored his playoff-leading 12th goal after Tampa Bay overcame an early 2-0 deficit.
The Rangers also came back after trailing 4-2, with Fast scoring his second goal late in the second period and McDonagh converting a power-play opportunity early in the third.
After splitting the first two games in New York, the Rangers talked about cleaning up mistakes that cost them in Game 2, as well as the need to create more scoring opportunities against Lightning goalie Ben Bishop.
They didn't have a lot of chances early, but did make the most of team.
Brassard scored on the first shot of the game, sending the puck over Bishop's shoulder from the left circle. Fast made it 2-0 with the nifty backhand made possible, in part, by a big hit on Tampa Bay's Matthew Carle. With the Lightning defenseman slow to get to his feet, Fast skated freely up the middle before taking a pass from Chris Kreider and barreling in alone on Bishop to score his second goal of the playoffs and give the Rangers the type of start they felt they needed to reassert themselves.
But Tampa Bay would not be denied.
Stamkos began the comeback with his fifth goal of the playoffs. Lundqvist cleared a bouncing puck with his stick directly to the high-scoring Stamkos, who had 43 goals during the regular season and is a two-time Maurice Richard Trophy winner. Johnson assisted on Palat's goal to make it 2-2, and the linemate returned the favor with a perfect pass through the middle to Johnson, camped to Lundqvist's right for an easy tap in that put the Lightning up 3-2.
Killorn increased the lead to 4-2 for all of 29 seconds. Fast's second goal of the night trimmed New York's deficit to one goal at 17:47, setting the stage for an entertaining third period.
McDonagh's power-play goal made it 4-4 less than 3 minutes into the period. Palat's second goal of the night put the Lightning back in front until New York pulled even again on Boyle's late goal.
Bishop finished with 23 saves for Tampa Bay. Lundqvist stopped 34 of 40 shots, giving up six goals for the second straight game.
Notes: Derek Stepan's assist on New York's first goal gave him a playoff career-best, six-game points streak. ... The Lightning went 1 for 2 on the power play, with the Rangers becoming the last team to allow a power-play goal on the road this postseason. ... Johnson tied Tampa Bay's record for most playoff goals in one year. Brad Richards and Ruslan Fedotenko both scored 12 during the Lightning's run to their only Stanley Cup title in 2004. ... Rangers RW Mats Zuccarello, who hasn't played since taking a shot off the helmet in Game 5 of New York's first-round series against Pittsburgh, skated after team practice for the second time this week. There's still no timetable for his return.