Seabrook fired a 45-foot shot past Bruins goalie Tuukka Rask to end Game 4 and send the series back to Chicago tied 2-2.
Seabrook also scored the overtime goal in Game 7 of the Western Conference semifinals to eliminate the Detroit Red Wings.
Only 12 total goals were scored in the first three games before the teams combined for 11 on Wednesday night.
Game 5 of the best-of-seven series is Saturday night.
It was the third overtime game of the series. The Blackhawks won the opener 4-3 in three overtimes, and the Bruins won 2-1 in the first overtime period in Game 2.
Boston grabbed the series lead Monday night 2-0 behind Rask’s third shutout of the postseason.
Seabrook’s shot from the right went to the far side of Rask, who appeared to be screened.
Trailing 4-3 after the second period, the Bruins tied it on Patrice Bergeron’s second goal of the game at 2:05 of the third period.
Patrick Sharp gave Chicago a 5-4 lead at 11:19 of the third period with the Blackhawks’ first power-play goal in 30 chances, but Boston came right back to tie it 55 seconds later on Johnny Boychuk’s hard 40-foot shot.
All five Bruins goals were to the glove side of goalie Corey Crawford.
Jonathan Toews broke his scoring slump in Chicago’s three-goal onslaught in the second period against Rask.
In an unusually wide-open game, the teams combined for five goals in the second period after the first ended in a 1-1 tie on goals by Chicago’s Michal Handzus and Boston’s Rich Peverley.
Patrick Kane and Marcus Kruger also scored for Chicago in the second. Milan Lucic and Bergeron countered for Boston.
Rask posted his third shutout of the postseason in Game 3 and began Game 4 with a shutout streak of 122 minutes, 26 seconds.
That ended at 129:14 when Handzus scored a short-handed goal at 6:48 of the first period. Then Peverley, who had been struggling offensively, scored his second playoff goal during a rare power-play shift for him at 14:43.
Toews and Kane led the Blackhawks with 23 goals each this season, and neither had scored a goal in the Cup finals. Toews had gone 10 straight games without one, but now has two goals in 21 playoff games.
His fortunes changed when he gave Chicago a 2-1 lead at 6:33 of the second. Michal Rozsival fired a low rising shot from the right point that Toews tipped in near the right post.
Just over two minutes later, Kane made it 3-1. Bryan Bickell shot the puck from low in the left circle. Rask deflected it to the other side and then scrambled to get back in position, but Kane converted the rebound at 8:41.
The Bruins stayed aggressive, and it paid off when Lucic got his sixth goal of the postseason at 14:43. Zdeno Chara passed the puck from the left boards to Lucic in the slot for a backhand from 10 feet past Crawford.
Then it was the Blackhawks’ turn to come back, and it took less than a minute.
Kruger put his own rebound past Rask for his third postseason goal this year at 15:32. But that 4-2 lead didn’t hold up for long in the back-and-forth game.
At 17:22, Bergeron scored his eighth goal of the playoffs off an odd bounce during a power play. Chara’s shot hit the glass behind Crawford and bounced back off the top of the net. It ended up in the slot, and Bergeron put it in to cut the deficit to 4-3.
Handzus had scored the first goal after Brandon Saad stole the puck from Tyler Seguin in the Boston zone and raced up the right side. He crossed the blue line and then passed across the slot to Handzus, who beat Rask from about 5 feet.
Then Peverley tied it. Bruins defenseman Andrew Ference kept the puck in the zone when he went to his knees at the left point. He passed it toward Peverley near the right circle. Peverley controlled the puck and took a shot from the inside edge of the circle, beating Crawford to the near side.
The Blackhawks, Stanley Cup winners in 2010, dominated the early part of the first period. But the Bruins, the 2011 champions, came on strong in the last 10 minutes and ended the period being outshot by only 10-9.
The Blackhawks won the opener 4-3 on Andrew Shaw’s goal at 12:08 of the third overtime and lost 2-1 in Game 2 on Daniel Paille’s goal at 13:48 of the first overtime.
Marian Hossa returned to the Blackhawks lineup after being a late scratch in Game 3 because of an upper body injury. He has three game-winning goals in the playoffs and was second on the team with 17 goals during the regular season.
Since the best-of-seven format for the Cup finals began in 1939, teams leading 2-1 have won the championship 38 of 47 times.
Boston had won its previous seven home playoff games, outscoring opponents 21-10. The Bruins are 11-3 in their last 14 games with all three losses coming in overtime.
Rask has allowed one goal or fewer in each of Boston’s last eight wins.