Since acquiring Taylor Hall and others at the trade deadline, the Bruins have won three straight games over the Islanders. The teams open their second-round playoff series on Saturday. Jeffrey T. Barnes/Associated Press

Just when the New York Islanders got finished with Jeff Carter lighting it up against them with Pittsburgh, they face another significant trade deadline pickup in Taylor Hall and the Boston Bruins.

The Islanders might not even be in the second round if not for a trade to get Kyle Palmieri and Travis Zajac from New Jersey. The Bruins also needed Mike Reilly arguably as much as Hall in the first round after their blue line was hit with injuries.

From Hall and Reilly to Palmieri and Zajac and David Savard with the Tampa Bay Lightning, trade deadline acquisitions big and small are already paying major dividends in the NHL playoffs.

As Stanley Cup-winning defenseman Ken Daneyko pointed out, “Obviously you hope for this when you make deadline acquisitions.”

“Sometimes you try and do too much, sometimes you’re trying not to step on anyone’s toes,” said Winnipeg’s Paul Stastny, who was a deadline addition for the Jets in 2018. “You were brought in here for a reason, and it’s not to change the game. Sometimes it’s tough because you know some guys might get moved around the lineup a little bit, but you try not to worry about that.”

Daneyko, now an NHL Network analyst, called Hall a “perfect fit” with the Bruins. Hall, the 2018 Hart Trophy winner as league MVP, scored two goals in five games of the first round against Washington — the same number he had in 37 games with lowly Buffalo before the trade to Boston.

One of those goals tied the score with 2:49 left in Game 2, which showed the Bruins how Hall could perform in important moments after never winning a seven-game series previously in his NHL career.

“A lot of things in life are about adjustments,” Hall said. “In the playoffs, you have to play hard, you have to play physical, you have to do all those things, but you also have to make plays and you also have to play with calm and composure.”

The Bruins can also play with more confidence thanks to Hall, who gives them secondary skill behind the “Perfection Line” of Brad Marchand, Patrice Bergeron and David Pastrnak. Hall has slid in on David Krejci’s left wing perfectly.

“Since they got Taylor Hall it’s really put everybody on the right seat on the bus, I think, for their team,” Islanders coach Barry Trotz said Friday. “It has given them (a) second line that is a threat, and night in and night out it can be a gamechanger, at times, for them.”

Much like Carter was a difference-maker with four goals for the Penguins, Islanders star Mathew Barzal called Hall a “game-breaker” New York must keep an eye on. The same goes on the other side for Palmieri, who scored the first-round Game 1 overtime winner and added a key goal in the series clincher.

Zajac, the other player the Islanders got from the Devils for a first-round pick, had been a healthy scratch until an injury opened the door for him to play Game 5 against Pittsburgh. Of course he picked up an assist on the winning goal.

“If we didn’t have a Palmieri or a Zajac, we’d be in one (a hole) a little bit,” Trotz said. “We’d be getting deep into our depth.”

The Bruins would be in trouble without Reilly after losing defensemen Jeremy Lauzon, Jakub Zboril and Kevan Miller to injury. Reilly called it “some kind of tough luck” — but it’s also a playoff lesson that a contender can’t have too many defensemen.

The Lightning figured that out on the way to hoisting the Cup last year, filtering players in and out amid injuries. They paid the price of a first-round pick this year to get rugged, big-minute defenseman David Savard from Columbus at the deadline.

Lightning coach Jon Cooper said facing Savard in the playoffs the past two seasons gave them “a firsthand look of him and what he can do.” The same goes for Toronto getting ex-Blue Jackets captain Nick Foligno, whose absence after the first two games against Montreal has hurt.

Savard didn’t play a leading role in Tampa Bay getting past Florida. But Daneyko said Savard is “going to have a bigger impact as these playoffs go along because of his size, because of his experience.” The Lightning are counting on that in a bid to repeat.

“It’s just one of those things that the more you play with a new group of faces, the better and better you get just because you start to understand guys’ tendencies and understand where they’re going to be on the ice,” said forward Blake Coleman, who was one of the Lightning’s 2020 deadline pickups. “Savvy’s a guy that we love having in our room and another guy that I expect to get better and better as we go.”

Not every trade worked out as planned: Anthony Mantha was ineffective for the Capitals, and Sam Bennett had as many suspensions as goals for the Panthers. And some deals long before the deadline worked out OK, like Winnipeg adding Pierre-Luc Dubois, who was a big part of a sweep of Edmonton.

“To try to get to know the systems, watch the team play, I think it was really important to get that time,” Dubois said. “I think it was really helpful for me to be here at that time and not necessarily two, three weeks, a month before the playoffs started.”