Brodeur, who signed a one-year contract with St. Louis on Tuesday, relieved an ineffective Jake Allen (three goals on 12 shots) to start the second period. He made 14 saves to earn his 689th career win in his sixth career relief appearance.
"Not what I expected, that's for sure," Brodeur said. "I think it's been a tough road trip. We played some tough teams.
"It's nice. First one out of the way so I'm excited about that. As a team, we've had stretches, part of the game that's been tough on us. Today was another one, but we didn't pay the price. Offensively we were awesome. We bailed out everybody who made mistakes and now we got a win, so it's definitely nice."
Blues forward Paul Stastny had two goals, including the go-ahead goal at 13:26 of the third period. Forward Joakim Lindstrom had three assists, and defenseman Kevin Shattenkirk had a goal and two assists and a game-high eight shots on goal to help the Blues rally from a 3-0 first-period deficit and avoid their first three-game losing streak of the season.
"It was a moment where it wasn't only that first period that we were really disgusted with ourselves about," Shattenkirk said. "It was the last two games before this. We haven't played our best hockey. We've looked almost lazy and haven't really played that smart, simple game we're so good at. That's what we were able to do there in the second period, go back to the basics and what makes us a strong team. Then we start to play and we look like the Blues that everyone kind of says that we are, the fast, hard-hitting, simple kind of blue-collar team."
The Blues (17-8-2), who finished a four game road-trip 2-2-0 and had lost consecutive games to the Chicago Blackhawks and Nashville Predators, converted three times on the power play after entering the game with no goals in their past 17 chances with the man advantage.
"We were organized and had good movement and lots of smart shots," Blues coach Ken Hitchcock said. "We really put a lot of pressure on [Islanders goalie Jaroslav Halak] with the shots that we were able to obtain from the top and that's a good sign. [Halak] saw a lot of traffic today. There were a lot of bodies in front of him today."
Halak made 34 saves in his first loss after a franchise-record 11 consecutive victories. New York had its three-game winning streak snapped and lost for the third time in its past 16 games. The loss kept the Islanders (19-8-0) in a first-place tie with Pittsburgh Penguins in the Metropolitan Division and was their first at Nassau Coliseum since Oct. 28, a run of seven straight victories.
"I don’t think we're going to panic," John Tavares said. "We know we have to be a lot better than we were tonight. Giving up six goals is unacceptable and just the way we played in general. It’s back to work on Monday and know we have to be better. We have a couple tough games on the road next week and we know we have to play better hockey."
St. Louis forward Vladimir Tarasenko provided the margin of victory at 17:32 of the third for his fifth goal in five games.
T.J. Oshie tied the game 10 seconds into a Blues power play when he received a pass from Shattenkirk and took advantage of a screen in front to beat Halak.
New York forward Frans Nielsen led a rush from the red line and found Kyle Okposo. After his shot was blocked, Okposo regained the puck and passed to Tavares, who skated through traffic to beat Brodeur on the backhand to give the Islanders a 4-3 lead at 19:06 of the second.
"That doesn't bother us," Hitchcock said. "When you play in the West every game is a one-goal game. You're up one, down one, you have to play. No lead is safe in the West. You have to fight right to the end and we had a lot of confidence if we fought to the end we could grasp control of the hockey game.
"Our deep game, the game that we're really capable of playing started to come back into our team again in a positive way. It's a good sign."
The Blues got on the board at 2:36 of the second period when Shattenkirk threaded a pass through traffic and found Stastny for his fourth goal.
Shattenkirk's power-play goal from the point tied the game at 3 after he received a cross-ice pass from Lindstrom.
The Islanders nearly took the lead with 10:51 left to play on Okposo's wraparound chance, but Brodeur was able to squeeze the puck under his armpit before it fell short of the goal line, which was confirmed by replay.
Nielsen opened the scoring with the Islanders on the power play. After Nick Leddy's shot from the point was blocked, Okposo corralled the rebound and made a no-look pass across the crease to Nielsen, who scored on the open net for his sixth at 7:57 and first in 12 games.
Islanders forward Ryan Strome took advantage of a giveaway from Shattenkirk late in the first. Strome's slap shot from the point beat Allen for a 2-0 lead at 18:01. A minute and 38 seconds later, Allen failed to control the rebound of Matt Donovan's shot and Grabner tipped it home.
The Blues were without forward Alexander Steen, a late scratch with a lower-body injury. Defenseman Carl Gunnarsson left the game with an upper-body injury after taking an Anders Lee elbow to the head.