The winner came after Boston's Patrice Bergeron won a faceoff in the offensive zone back to Zdeno Chara. The Bruins captain then fed Seidenberg, whose shot found its way past Senators goalie Robin Lehner through a maze of players.
Kaspars Daugavins scored the lone goal for the Senators (16-9-6), who saw a three-game winning streak come to an end.
Lehner made 27 saves in taking the loss.
The Senators haven't defeated the Bruins at Scotiabank Place since April 7, 2009. Boston has also taken 12 of the last 13 encounters overall, including the first three this season.
After an uneventful first period, Daugavins opened the scoring at 4:55 of the second with his first goal of the season on a shot from the side boards that beat Khudobin high.
Daugavins was the talk of the NHL for his ringette-style spin-o-rama move that failed to connect in the shootout when the two teams last met on March 11.
His goal on Thursday ignited the 19,603 on hand, but the crowd was deflated after Paille beat Lehner just over one minute remaining in the period.
The Senators had a couple of great chances to regain the lead in the dying seconds, but Khudobin made some solid stops to keep the score tied.
With an assist on Daugavins' goal, Sergei Gonchar extended his point streak to nine games. He also set a new franchise record for defencemen with assists in nine straight games.
Thursday's game marked the first in a five-game homestand for the Senators. Ottawa hosts the Tampa Bay Lightning on Saturday afternoon.
Notes: The Senators C Jim O'Brien was a healthy scratch. Ottawa was also without G Craig Anderson (ankle sprain, indefinite), LW Dave Dziurzynski (concussion, indefinite), D Erik Karlsson (Achilles, out for the season), C Jason Spezza (upper body injury, indefinite), LW Milan Michalek (knee, indefinite) and D Jared Cowen (hip, out for the season). ... C Ryan Spooner played his first NHL game in his hometown for the Bruins. Boston was without C Chris Kelly (broken tibia, indefinite) and D Adam McQuaid (shoulder, three weeks). C Rich Peverley and LW Lane MacDermid were a healthy scratches.