Perrin added another goal in the third period, and Filip Kuba scored twice as the Lightning scored five goals for the third straight game.
St. Louis stretched his point streak to nine games when he fired in a hard shot off a feed from Perrin that gave Tampa Bay a 2-1 lead with 7:12 left in the middle period. The pair, who grew up in Laval, Que., went on to star together at the University of Vermont but had never combined on an NHL goal.
Vincent Lecavalier got the other assist, giving him points in nine straight games, too. Tampa Bay won for just the second time in six games (2-3-1), with rookie Johan Holmqvist in net for both.
Kuba extended the lead to 3-1 with another power-play goal in the second period. It was his first tally with the Lightning, who signed the defenceman away from the Minnesota Wild in the off-season. Kuba added another man-advantage goal with 7:05 remaining to give Tampa Bay a three-goal lead.
Perrin made it 5-1 with 4:28 left.
Alexei Zhitnik scored for the Islanders.
Tampa Bay rode two early-season trends to victory.
The Lightning pulled away in the second period - a frame they have owned through 15 games. With the two goals against New York, they have outscored opponents 25-9 in the second period. Tampa Bay also improved to 7-1-1 when scoring at least three goals this season.
Zhitnik got the Islanders even 1-1 with 55.5 seconds left in the first period, beating Holmqvist with a shot from the left point that fluttered through traffic and ticked off the glove of the goalie before finding the net.
That was the only blemish for Holmqvist, who won consecutive starts in a span of five days. He earned his only other NHL win Thursday with a 32-save effort at Philadelphia. Perrin sealed the 5-2 victory with an empty-netter, the first of his two NHL goals.
Perrin can count all of his points on one hand - his goal and assist gave him five in his career. In contrast, St. Louis has 151 regular-season goals, 337 points, and an MVP trophy on his resume.
As far as Perrin is concerned, St. Louis' biggest assist came in 2003 when the star forward suggested to general manager Jay Feaster that the Lightning sign Perrin, who was playing in Finland.
Now they are back together and are roommates on the road. Feaster smiled broadly in the press box Monday when the goal was scored and jokingly suggested the Vermont fight song be played as he team celebrated.
Holmqvist did the rest in place of regular goalie Marc Denis, who has lost three straight starts. He finished with 25 saves.
Mike Dunham stopped 22 shots, but took the loss while spelling Rick DiPietro. New York's top goalie, who signed a 15-year contract before the season started, heard boos and calls for Dunham in the Islanders' 4-1 home loss to Atlanta on Saturday.
Notes: Tampa Bay is 0-6 when scoring two goals or fewer. . . . St. Louis earned an assist on Kuba's second goal . . . The Islanders went 5-3-2 while playing nine of 10 at home. They start a five-game road trip Thursday at Philadelphia. . . . Perrin also had a playoff assist during the Lightning's run to the Stanley Cup title in 2004. . . . The Lightning swept the four-game series from New York last season.