The Lightning don't play again until next Friday, when they face the Buffalo Sabres at Ericsson Globe in Stockholm as part of the 2019 NHL Global Series.
"Eventually we're going to get rewarded and then hopefully we can go on a little bit of a streak here," Tampa Bay coach Jon Cooper said. "We are seeing improvement in a lot of areas, so we've just got to weather through this. We knew this was coming. … But we're still above .500 heading into Sweden and hopefully we can come back with some more points and then dig our heels in once our schedule evens out."
The Lightning had the puck for most of the first 12 minutes of the third period and held a 11-2 advantage in shots on goal in that time. But the Islanders kept them to the outside and killed off a penalty to withstand Tampa Bay's surge until they could catch a break.
A dump-in bounced off McDonagh and popped free. Lee got the puck and moved it across the ice to Barzal, who passed to Bailey for a one-timer from the right circle that gave the Islanders a 3-1 lead at 7:19.
"That's tough," Lightning forward Alex Killorn said. "That's a huge moment in the game for us to get some momentum going the other way. That's just the way things are going for us now."
Lee gave New York a 4-1 lead at 14:27. Johnny Boychuk had the assist to extend his point streak to four games.
McDonagh scored a 6-on-5 goal at 18:03 to make it 4-2, but Brassard scored for the fourth straight game, an empty-net goal at 19:24, for the 5-2 final.
"I think we frustrated them by playing a 200-foot game," Islanders coach Barry Trotz said. "We made them go through us. We were like, 'We're going to stay on top of you, we're going to play our game, not play your game. You're better at your game then we are, so force you into our game if we can.' We're comfortable there."
Barzal scored his second goal in as many games to give the Islanders a 1-0 lead at 4:58 of the second period.
Gourde scored 2:51 later with a near-side backhand from low in the right circle tie the game 1-1 at 7:49.
New York took a 2-1 lead on Ryan Pulock's one-timer through traffic from the right point at 11:33 of the second. Pulock has scored in back to back games.