Chicago never trailed in the high-scoring battle, but Boston rallied to tie the game on three occasions in a bid to move within one win of the Stanley Cup.
The winning shot, however, went Chicago's way when Seabrook fired one past Tuukka Rask.
Seabrook's goal came after Rask had stopped a shot by Patrick Kane. The rebound came to the left point, where Bryan Bickell gained control. His pass into the low slow bounced off two defenders and drifted to Seabrook, whose blast beat Rask to the stick side.
Rask has allowed 10 goals in the two Boston losses in the NHL championship series. In his seven previous playoff wins he has given up a total of four goals with three shutouts.
Boston's Patrice Bergeron was the only player with more than one goal in the game, scoring late in the second period and early in the third while rallying the Bruins into a 4-4 tie. Bergeron has nine goals in the playoffs.
Patrick Sharp then scored a power-play goal that gave the Blackhawks the lead with 8:41 left in the regulation, but Johnny Boychuk sent a slap shot past Corey Crawford with 7:46 remaining to again tie it.
Rask made 41 saves and Crawford stopped 28 shots.
The 11 goals in the game were just one short of the total scored in the first three games of the series combined. Three of the opening four contests have gone to overtime.
Chicago regained home-ice advantage and will host Game 5 Saturday.