Seguin scored at 3:17 of overtime, Thomas made 36 saves, and the Bruins beat Washington 4-3 on Sunday to tie the first-round Eastern Conference playoff series at three games apiece.
The defending Stanley Cup champion Bruins never trailed, but needed a stolen pass and a deft bit of skating by Seguin to finally get the decisive goal and avoid elimination.
The series finale is Wednesday night in Boston. The first six games were all decided by one goal, three of them in overtime.
"It's been a dogfight from start to finish," Bruins coach Claude Julien said. "Both teams here are heading to Game 7 with the same kind of confidence. For us, it's time to take advantage of the home ice that we've fought hard all year to get. We've got to make it count."
Seguin led the Bruins during the regular season with 29 goals and 67 points but was scoreless in the playoffs until Sunday. Thomas, a two-time Vezina Trophy winner, was generally outplayed by Capitals rookie Braden Holtby over the first five games of the series.
Not so in Game 6.
Thomas had 35 saves in regulation, and Seguin contributed an assist before beating Holtby to end the game.
"It was a coming-of-age goal there in overtime," Thomas said about Seguin, a 20-year-old with two years of NHL experience.
Seguin veered slightly to his right to draw Holtby from the net, then lifted a shot past the rookie to win it.
"I saw the goalie challenging, so I just tried to make a quick move and got lucky it went in," Seguin said. "This series I've had a lot of chances and opportunities and I haven't been finishing them off. It's just really nice to get that feeling of finding the back of the net."
Julien said, "For him to jump on that and be patient enough to skate around the goaltender, it's great to see."
That kept alive Boston's bid to become the first team to win successive Stanley Cups since the Detroit Red Wings in 1997-98.
The seventh-seeded Capitals, on the other hand, face the prospect of having to win a third game in Boston to advance to the second round.
"Game 7 is a grinding kind of game," coach Dale Hunter said. "We're used to playing it. Every game here has been tough game. Both sides are, I imagine, a little bit banged up. But little bruises, they'll forget about them come Game 7."
The Bruins took a 3-2 lead at 11:51 of the third period on a goal by Andrew Ference, who put in the long rebound of a shot by Seguin. Ference thrust his fist into the air in delight in front of the Bruins' bench to celebrate after his first goal of the series.
But Washington wasn't done. Off a faceoff in the Boston zone, Alex Ovechkin controlled the puck with his left skate and promptly ripped a shot that skidded between Thomas' legs with 4:52 left in regulation.
It was not unlike Saturday's game, when Thomas gave up a lamentable goal to Troy Brouwer in the closing minutes of Washington's 4-3 victory.
Julien knew Thomas would bounce back Sunday, and the coach was right.
"I thought he played a huge game," Julien said. "I knew he was upset (Saturday) after the game. Just by his reaction, I had no doubt he was going to come up huge today."
Boston's Rich Peverley opened the scoring at 5:56 of the first period by deflecting a shot by Ference past Holtby. It was the first time in five games and only the second time in the series that the Bruins notched the game's initial goal.
The lead was short lived. After gaining possession of the puck on top of the left circle, Washington defenseman Mike Green twice drew his stick back before choosing the right moment to launch a slap shot that soared past Thomas' left shoulder and into the net at 9:47.
But the Bruins went up 2-1 7 minutes later on a power-play goal by Krejci, who ended Boston's 1-for-16 struggle with the extra man. Krejci entered the center of the Washington zone, dropped a pass to incoming Lucic on the left side and then tipped in the return pass.
In the second period, however, the Capitals' penalty-killing efficiency came heavily into play. After Ovechkin received a 4-minute penalty for bloodying the nose of Zdeno Chara with a high stick, Washington limited the Bruins to a single shot on goal while short-handed and even managed a decent shot of its own.
The Capitals pulled even with less than a minute left in the period. Backstrom charged down the right side and waited until Thomas and Chara committed themselves before sending a backhand, cross-ice pass to Jason Chimera, who slammed the puck into the net before Thomas could move back across the crease.
Washington outshot Boston 15-5 in the second period. It will take that kind of effort for the Capitals to prevail on Wednesday.
"We've already seen them six times. I don't think anything's going to change on our end," said Washington's Matt Hendricks, who was not surprised at Boston's effort Sunday.
"They're Stanley Cup champs last year. They're not going to die easy."
Bruins D Joe Corvo was scratched after being struck in the right knee by a puck Saturday ... This is the third time the teams have met in the postseason. Each has won eight games ... Washington's Alexander Semin was held without a goal for the first time in four games.