The Bruins (45-17-10) joined the Tampa Bay Lightning from the Eastern Conference. The Nashville Predators are the only team to secure a spot in the postseason from the Western Conference.
"Getting that goal, getting that one playoff point, it's huge for us," said Bruins forward Ryan Donato, who scored his second goal in his second NHL game. "Obviously, this wasn't the result we wanted, but we're where we want to be."
[WATCH: All Bruins vs. Blues highlights]
Jaden Schwartz scored 30 seconds into overtime to give the Blues their third win in a row, fifth in six games, after he tied it 1-1 at 9:36 of the third period.
Schwartz won the game when he collected the puck from defenseman Colton Parayko behind the Blues net, moved up through the middle of the ice, and used Bruins defenseman Matt Grzelcyk as a screen to beat goalie Anton Khudobin (18 saves) with a wrist shot low to the stick side.
"Colton gave it to me behind the net, and I knew I had some space, just tried to pick up some speed and see what was going to develop," Schwartz said. "The one guy kind of went with [Brayden Schenn]. I kind of had a little 1-on-1, just tried changing the angle and getting it through the guy's legs."
St. Louis (40-29-5) is two points behind the Los Angeles Kings for the second Western wild card into the playoffs and three behind the Colorado Avalanche for the first wild card.
Video: #ThirstForTheCup: Bruins punch ticket to the playoffs
The Blues have won each game in their winning streak in overtime after trailing entering the third period. They were 2-23-1 in the 26 previous games they trailed after two periods.
"We knew it was in there, but obviously, we're finding it at the right time at least," Blues coach Mike Yeo said of their resolve.
"We know if we lose a game or lose a couple, we might be out of it," said St. Louis goalie Jake Allen, who made 21 saves. "So, it's just points right now."
Boston trails Tampa Bay by four points for first place in the Atlantic Division and leads the Toronto Maple Leafs by seven for second. The Bruins have a game in hand on each.
Donato, who signed a two-year contract with Boston on Sunday after completing his junior season at Harvard, gave the Bruins a 1-0 lead at 10:12 of the first period with a power-play goal. Blues defenseman Alex Pietrangelo tried to clear the puck, but it caromed off referee Brad Watson and onto Donato's stick in the slot.
Video: BOS@STL: Donato cashes in on key bounce for PPG
"I thought it was weird because I don't know where [Watson] is," Pietrangelo said. "Just turned and tried to get the puck out on the penalty kill. Oh well, stuff happens."
The Bruins, who are 2-2-2 in their past six games, fell to 29-0-4 when leading entering the third period.
"We talk about puck possession," coach Bruce Cassidy said. "We had it, and we gave it away. You're always happy to be in the game and get that one point, but when you have a lead going into the third, you want to close."
Goal of the game
Schwartz's goal 30 seconds into overtime.
Video: BOS@STL: Schwartz goes coast-to-coast for OT winner
Save of the game
Allen stopping Tommy Wingels at 12:43 of the second period.
Video: BOS@STL: Allen fights off Wingels' wrister
Highlight of the game
Schwartz's goal at 9:36 of the third period.
Video: BOS@STL: Schwartz ties game with slick wrister
They said it
"It's Step One. Going into the season, we wanted to make the playoffs, be a Stanley Cup contender and at some point hope you're a Stanley Cup favorite. That's kind of where it goes from there. But right now, we got in, so we're going to be a contender, and that's the good news. Going forward, we want to be in the best position possible, playing the best hockey going in." -- Bruins coach Bruce Cassidy on making the playoffs
"We're resilient, showing character. You try and build throughout the game and get opportunities to get goals and wear teams down. As the second period went on into the third period, we felt like we wore them down. We were going to have a good opportunity to score." -- Blues captain Alex Pietrangelo
Need to know
The Bruins were without forwards Rick Nash (upper body), Jake DeBrusk (upper body), Patrice Bergeron (fractured foot) and David Backes (leg laceration), and defensemen Zdeno Chara (upper body), Torey Krug (undisclosed) and Charlie McAvoy (sprained MCL); Krug was a late scratch. That's 234 points (83 goals, 151 assists) missing from their lineup. ... Boston is in the playoffs for the ninth time in 11 seasons and 71st in its history. ... Blues right wing Vladimir Tarasenko (upper body) missed a second straight game. … Schwartz's game-winning goal was his third this season, 15th of his NHL career. It was his fourth NHL overtime goal.
Bruins: At the Dallas Stars on Friday (8:30 p.m. ET; SNE, SNW, FS-SW, NESN, NHL.TV)
Blues: Host the Vancouver Canucks on Friday (8 p.m. ET; FS-MW, SNP, NHL.TV)
Video: Schwartz's pair leads Blues to 2-1 win in overtime