"This means a lot to a lot of people," Carolina captain Justin Williams said. "It means a lot to me, it means a lot to everyone here, everyone watching at home, everyone on the radio. And it means a lot to our players as well."
Sebastian Aho and Teuvo Teravainen each had a goal and an assist, and Curtis McElhinney made 26 saves for the Hurricanes, who will face the Boston Bruins or the Columbus Blue Jackets. That series is tied 2-2 entering Game 5 at Boston on Saturday (7:15 p.m. ET; NBC, CBC, SN, TVAS).
[WATCH: All Islanders vs. Hurricanes Game 4 highlights | Complete series coverage]
It is the first sweep of a best-of-7 Stanley Cup Playoff series in Carolina/Hartford Whalers history. The Hurricanes have advanced to the conference final in four straight playoff appearances (2002, 2006, 2009). Carolina also has won six straight playoff games since losing Game 5 to the Washington Capitals in the first round.
Video: #ThirstForTheCup: Carolina surges to Conference Final
Mathew Barzal scored for the Islanders, who swept the Pittsburgh Penguins in the first round. Thomas Greiss made nine saves in relief of Robin Lehner, who made eight saves on 11 shots.
The Islanders are the fourth NHL team to be swept in the second round after winning by sweep in the first round.
"You think about [how] we've had success all year, it's being able to shut down other teams," New York coach Barry Trotz said. "Counter, frustrate them, all that. They did a lot of that to us. When you're pressing, we usually counter, and they did that against us. We were chasing the whole series."
Barzal made it 1-0 on the power play at 2:30 of the first period when he tucked a rebound past McElhinney.
Video: NYI@CAR, Gm4: Barzal jams home rebound for PPG
Aho answered with a power-goal to tie it 1-1 at 4:44. Lehner stopped Aho's shot at the right post, but Islanders defenseman Adam Pelech pushed the rebound through the legs of Hurricanes center Jordan Staal and past his goalie.
"To get one right back stole the momentum," Carolina defenseman Justin Faulk said. "Getting ourselves evened up before the end of the first (period) was huge."
Teravainen gave the Hurricanes a 2-1 lead at 2:11 of the second period. After Aho forced a turnover on Pelech behind the Islanders net, Warren Foegele passed across the slot to Teravainen for a shot into an open net.
Greg McKegg scored his first playoff goal at 3:17 to make it 3-1. Lehner made a glove save on Brett Pesce's shot, but the rebound fell to the ice, and McKegg scored through the five-hole.
Video: NYI@CAR, Gm4: McKegg beats Lehner with tap-in tally
Lehner was pulled after the goal. He has never defeated the Hurricanes (0-5-0).
"I know myself, I felt really good coming in," Lehner said. "It was kind of a weird first period, but they came out flying in the second period, and that was that."
Trotz said of changing goalies, "Goals had been pretty hard to come by in this series, and we couldn't let it get past three. I just felt that hopefully it could quiet it down, maybe guys would focus in for [Greiss]. We just couldn't get close enough in the end."
The Hurricanes extended the lead to 4-1 at 8:51 after Jordan Staal lifted a pass to Williams, who scored on a backhand for his 100th playoff point (39 goals, 61 assists).
"We came out and imposed our will on them early (in the second period), scoring a goal," Williams said. "You just have to create doubt in them, and we did that at the start of the second and carried it on. And McElhinney, as usual, not surprised, he was there when we needed him, made some big saves and it was great."
McElhinney earned his third straight win since replacing the injured Petr Mrazek in the second period of Game 2.
"Obviously we knew it was going to be a tight game," McElhinney said. "To get a couple extra goals and sit with that lead going into the third felt great."
Andrei Svechnikov scored off the rush to make it 5-1 at 15:13 of the third period.
Video: NYI@CAR, Gm4: Svechnikov tacks on insurance goal
Brock Nelson scored on a wrist shot with 1:09 remaining for the 5-2 final.
The Hurricanes outscored the Islanders 13-5 in the series, allowing two even-strength goals.
"I'm just so proud of these guys, I can't even tell you," Carolina coach Rod Brind'Amour said. "We had a good push, and that was enough. All the games in the series, we never felt like we could get to our game for any length of time, but there were segments, and we were able to capitalize on those kind of time frames."
They said it
"You've got to give this team a lot of credit; [heck] of a hockey team, probably one of the best in the League since Christmas moving forward. They're hard to play against. They're really, really detailed. They beat us fair and square. It probably was tighter than 4-0. A bounce here, a bounce there, but honestly, they were the better team." -- Islanders goalie Robin Lehner
"It's taking pride in how they do things, who they're doing it with. They just come to work, man. They earn everything that they're getting right now. That's what makes me the most proud. It's not always going to be pretty, but it's not from a lack of commitment or digging in." -- Hurricanes coach Rod Brind'Amour
Need to know
With nine playoff points (five goals, four assists), Foegele is tied with Erik Cole (2002) for the most by a rookie in Hurricanes/Whalers history. … Before Aho's goal, Carolina had not scored on 23 straight power plays dating to Game 3 against Washington. … Jordan Eberle had an assist, giving him at least one point in seven of the New York's eight playoff games (nine points; four goals, five assists). ... The Chicago Blackhawks (1970, 1972) and the Buffalo Sabres (1993) were swept in the second round after sweeping in the first.
Islanders: Season over
Hurricanes: Game 1 of Eastern Conference Final against Boston Bruins or Columbus Blue Jackets (TBD)
Video: Hurricanes finish sweep of Islanders, advance to ECF