Hedman scored twice and Bishop stopped 28 shots Sunday, helping the defending conference champions beat the New York Islanders 4-0 and end their second-round playoff series in five games.
The Lightning advanced by winning four straight after dropping the series opener at home. They also eliminated Detroit in five games in the opening round, making them 2-0 in close-out situations this post-season.
"I think we learned last year we had a couple of series where we had chances to close (opponents) out at home and we kind of let them slip," Bishop said. "We really wanted to take pride in closing teams out this year."
Hedman scored an unassisted goal from the slot at 13:49 of the first period, then beat Islanders goaltender Thomas Greiss again on a second-period power play that gave Tampa Bay a three-goal lead.
"Brutal. It's hard to believe it's over," Islanders captain John Tavares said. "You put a lot into this and we didn't accomplish what we set out to do."
Nikita Kucherov and Brian Boyle also scored for the Lightning, who will face either the Pittsburgh Penguins or Washington Capitals in the East final. The Penguins lead that series 3-2, with Game 6 Tuesday night in Pittsburgh.
"Back to back, it's pretty impressive what our guys have done," Tampa Bay coach Jon Cooper said. "Once you get there, you want to get back. I'm really impressed with our drive. We didn't play perfect playoff games every time, but we're getting contributions from everybody in the lineup. If you want to win, you need that."
The 6-foot-7 Bishop earned his fifth career playoff shutout, fourth in the deciding game of a series. He blanked Detroit 1-0 in Game 5 to end that first-round matchup and won two Game 7s without allowing a goal to help Tampa Bay reach the Stanley Cup final last year.
The loss ended New York's deepest playoff run since 1993.
Tavares led the Islanders to a thrilling six-game victory over the Florida Panthers in the opening round. He had a goal and assist in New York's only victory over Tampa Bay, but didn't have a point in the last four games.
"It will sting for a long time, but you have to get over it," said Greiss, who stopped 21 of 25 shots.
The series was much more competitive than the final result would suggest.
The Islanders let third-period leads slip away in Game 3 and 4 in Brooklyn. Kucherov had tying goals in both games before Boyle and Jason Garrison provided winning goals in overtime to thrust the Lightning into a 3-1 series lead.
"We obviously played some good hockey at times, but we just let those two games at home slip away. That put us behind the 8-ball for (Sunday)," Tavares said.
There was little drama in the clincher, with Hedman and Boyle scoring within a five-minute span of the opening period before Hedman's second goal — fourth this post-season — made it 3-0.
Tampa Bay defeated the New York Rangers in last year's conference final, earning its second trip to the Stanley Cup final.
They've done it with Bishop playing like a Vezina Trophy finalist and Kucherov, Tyler Johnson, Alex Killorn and young Jonathan Drouin, who had an assist on Hedman's second goal, making timely contributions.
Kucherov's breakaway early in the third period was his NHL-leading ninth goal of the playoffs.
"Last year was a good experience for me and the team. You know what to expect," Hedman said. "You want to be at your best when you come to the playoffs. We battle for each other, and that's paying off right now. We've got to keep that going."
Notes: After playing 26 of a possible 28 games during last year's playoff run, it has only taken the Lightning 10 games to get back to the Eastern Conference final. ... Bishop earned his 21st playoff victory with Tampa Bay, tying Nikolai Khabibulin for most in franchise history. ... Tavares and Hedman, who set a Lightning record for points for a defenceman in a playoff series with eight, were the first two picks in the 2009 NHL draft. ... Tavares had five goals and four assists in the Islanders' first-round win over Florida.