It also avenged last year's defeat to the Flyers, one in which the Bruins made a dubious entry into the NHL record books.
"It's disappointing. I'm not sure what went wrong," said captain Mike Richards, who had one goal in 11 playoff games. "They played extremely well."
Rich Peverley screened Bobrovsky on Boychuk's goal, which was set up by yet another faceoff win by the Bruins, who won the best-of-seven series, four games to none. The shot may have deflected off the stick of Flyers winger Scott Hartnell before it went past Bobrovsky.
Milan Lucic's second goal of the game, on a breakaway with 4:57 remaining, iced the win.
With the victory, the third-seeded Bruins advance into the conference finals against fifth-seeded Tampa Bay.
For the second-seeded Flyers, it was the first time they were swept in the playoffs since the 1997 Stanley Cup Finals against Detroit. "A choking situation," Flyers coach Terry Murray called that meltdown.
For the Bruins, it avenged The Humiliation - last year's collapse in which they became the first team in sports history to cough up a three-games-to-none series lead and a 3-0 lead in Game 7.
The Flyers were outscored in this series, 20-7.
Including the regular season, Boston went 7-0-1 against the Flyers since last year's playoff foldup.
The Bruins did a much better job containing James van Riemsdyk in the last two games of the series. It seemed like the young winger had a scoring chance every time he was on the ice in Games 1 and 2.
"They did a smarter job with the puck, and we didn't have as many odd-man rushes and chances off the rush and in transition" in the last two games, van Riemsdyk said.
Pronger missed the last three games with an unspecified injury. Would a healthy Pronger have made a difference?
"His track record speaks for itself, so I guess we'll never know," van Riemsdyk said.
Defenseman Sean O'Donnell said the Flyers didn't want to use Pronger's absence as an excuse, pointing out that the Bruins were missing Marc Savard, and the Penguins played without stars Evgeni Malkin and Sidney Crosby.
"Everyone's dealing with injuries right now," he said. "We showed during the year we were a good team when Chris wasn't in the lineup."
Said coach Peter Laviolette: "You notice the impact a guy like [Zdeno] Chara has on the other side, and you certainly miss him, but I don't want to use that as an excuse. We have [other] good players in the lineup."
Trailing 1-0 and having mustered just nine shots in the first 33-plus minutes, the Flyers capitalized on rookie Brad Marchand's turnover to knot the score with 6:38 left in the second period.
"It seemed like we were playing from behind a lot, and we put ourselves behind the eight ball," O'Donnell said.
Richards, on a two-on-one, made a deft pass to Kris Versteeg and then shielded off defenseman Dennis Seidenberg. That allowed Versteeg to go in alone, and he beat goalie Tim Thomas with a backhander for his first goal in 11 playoff games.
Thirty-two seconds after Versteeg's goal, the Flyers got a power play but failed to convert, and the teams went into the third period tied at 1-1.
A year ago, the Flyers scored a 5-4 overtime win over the visiting Bruins in Game 4, starting an improbable journey that took them to within two victories of the Stanley Cup.
The Bruins were intent on closing the series and erasing the ghosts of their 2010 collapse. They had more energy that the Flyers in the opening half of the first period, and took a 1-0 lead on Lucic's tap-in while on the power play.
It was the first goal in 21 games for Lucic, who knocked in a goalmouth pass from Nathan Horton. Goalie Sergei Bobrovsky, making his first start since Game 2 of the Buffalo series, had no chance.
Lucic scored while Dan Carcillo was in the penalty box for cross-checking, one of five Flyers penalties in the period.
The Flyers were facing elimination, but it was the Bruins who looked like the more desperate team in the opening period as they outshot the visitors, 13-6, and Bobrovsky was forced to make a handful of difficult saves.
Desperate? Until Danny Briere fired at Thomas with 11 seconds left in the first, the Flyers were outshot, 11-0, during a 14:23 span.
The Flyers, who had been given a stirring speech by Laviolette before practice Thursday, got a power play with 7.3 seconds left in the first period after Chara decked Scott Hartnell. Chara got a double-minor, while Hartnell received a minor.
With the menacing 6-foot-9, 260-pound Chara off the ice, the Flyers figured to be able to apply pressure when the power play carried into the second period.
Didn't happen. The Flyers had zero shots on the power play. Zero.
Contact staff writer Sam Carchidi at scarchidi@phillynew.com. Follow on Twitter at twitter.com/BroadStBull
