The change slowed things down for the remainder of the period; New York limited Tampa Bay to one shot on goal after the switch. But Lightning forward Yanni Gourde scored his first of two goals 4:03 into the second to make it 4-1, and Point scored on the power play at 13:18 for a 5-1 lead.
Tampa Bay did not miss the net on any of its shot attempts until forward Cedric Paquette shot wide with 1:07 remaining in the third period.
Point (two goals, three assists) and Kucherov (one goal, four assist) each had five points.
"We gave them a little too much space, plain and simple," Trotz said. "[We were] watching rather than participating too much. You can't do that against Tampa."
Varlamov started 14 of the first 16 games for New York this postseason. He entered the conference final 9-4 with a 2.00 GAA, a .921 save percentage and two shutouts but allowed nine goals on 63 shots in his past two games, both overtime losses that allowed Philadelphia to tie the series.
Greiss and Varlamov alternated the first 33 starts of the regular season before Varlamov seized the No. 1 job.
Greiss was 16-9-4 with a 2.74 GAA and a .913 save percentage in 31 games (29 starts) during the regular season. He will be an unrestricted free agent after this season.
Varlamov, who is in the first season of a four-year contract, was 19-14-6 with a 2.62 GAA, a .914 save percentage and two shutouts in 45 games (39 starts).
Regardless of which goalie starts Game 2 against the Lightning, the Islanders know they have to tighten things up defensively if they hope to advance to the Stanley Cup Final for the first time since 1984.
The Islanders last allowed eight goals in a playoff game in an 8-3 loss to the Flyers in Game 2 of the 1980 Cup Final, which the Islanders would go on to win in six games.
"I mean, it's never good to get blown out. It's embarrassing," New York forward Matt Martin said. "We didn't envision that, obviously. But at the end of the day, Game 2 is now the most important game. We don't want to go down 2-0 to a very good hockey team, so our goal is to get a split here and obviously we're playing on the same ice, but they do have the home-ice advantage in the series. If we go 1-1 with us getting last change, at the end of the day we would be happy with that.
"We'll put this one behind us. I still have a ton of confidence in our team and our group. We'll move forward and correct some things and get back on the wagon."