The rally came after Rochester scored a pair of third period goals 51 seconds apart to fight back from a 5-3 disadvantage, including Kevin Sundher's first professional tally, which tied the game at five and sent the game to overtime.
Four different players recorded multiple point nights, including Brennan (1+1), Hodgson (0+2), Mark Mancari (0+2) and team captain Kevin Porter (1+1). David Leggio made 34 saves through regulation and overtime before denying the final three Binghamton shooters.
Patrick Wiercioch, Hugh Jessiman and Andre Benoit each scored a goal and added an assist for the B-Sens, while goaltender Ben Bishop made 36 stops in the losing effort.
The goal was Rochester's third power-play tally in its last two games and gives Hodgson assists in back-to-back games since returning to the lineup after a 14-game absence. Brennan, who also earned an assist on the play, extended his current point streak to four games, collecting one goal and four assists over that span.
Rochester doubled its lead to 2-0 just 28 seconds later thanks to a defensive breakdown that led to Luke Adam's seventh goal of the season. Porter led the rush out of the Amerks zone up the right wing boards and left the puck for a streaking Mancari at center ice. After beating a defender at the Binghamton blueline, Mancari found Adam breaking in from the left side and he sent a quick shot on goal.
Bishop would make the initial save on Adam, but failed to control the ensuing rebound. Senators defenseman Tyler Eckford attempted to corral the puck back to Bishop, but the puck trickled through the netminder's legs and over the goal-line for the goal. Adam, who was the last Amerk to have possession, would get credit for the goal, thus extending his season-long point streak to seven games (5+3).
Binghamton evened things up on a goal from Eckord 4:43 into the second stanza to make it a 2-2 game. As Binghamton broke into the Rochester zone, David Dziurzynski left a drop-pass for Eckford, who unleashed a slap-shot from the top of the right face-off circle. The shot glanced off a stick in front of the net and deflected high into the Rochester net to even up the score.
The game would remain tied for only a few minutes, though, as Porter restored Rochester's lead, converting on Mancari's pass from the low slot to make it a 3-2 game. Mancari intercepted a pass at the Binghamton blueline, skated in along the left wing boards and found a wide-open Porter, who beat Bishop with a quick shot inside the near post. With the assist, Mancari also shows points in back-to-back games and has recorded five points (1+4) over his last four games, including a pair of multi-point outings.
Wiercioch gave the B-Sens a two-goal cushion with another power-play goal at 8:58 of the third period. Mike Hoffman's shot from the left point went wide of the net, but the rebound recoiled to Wiercioch off the end boards and, using the sprawled Leggio to his aid, banked the puck off the netminder's left pad to make it 5-3 contest.
Rochester certainly didn't let the deficit stand as the Amerks rallied with a pair of goals 51 seconds apart to knot the game at five apiece. Brennan countered first with his team-leading 11th goal of the season, and second in as many games, picking the top corner from the left face-off. Not more than a minute later, Sundher's first professional goal made it a 5-5 game as the rookie forward made a diving play to sweep in Maxime Legault's rebound in the low slot.
After a scoreless overtime, Hodgson sealed the deal with the game-winning goal in the shootout to propel the Amerks to a 6-5 win over the Baby Sens.
The same two teams will be in action again as the home-and-home series shifts to the southern tier on Saturday, Dec. 22 for a 7:05 p.m. bout at Broome County Veterans Memorial Arena.