Instead, RPI scored three goals in the third period, including an empty-netter with 54 seconds to go, for a 5-3 victory.

“In the third period, we were afraid to lose, and we lost,’’ said Parker. “We got run out of the building.’’

The Terriers welcomed a wounded Rensselaer squad that had lost four straight. BU had been struggling also, having won just once in their last six contests.

At the opening puck drop, the defending national champs went directly for RPI’s jugular. That almost proved costly when freshman Max Nicastro was tagged for an early penalty. But the Terriers forced a turnover in the RPI end. Kevin Shattenkirk intercepted a weak clearing pass and rifled a cross-ice pass to Chris Connolly. The BU sophomore calmly slipped the puck across the slot to an unmarked Nick Bonino, who roofed a shot past RPI freshman netminder Bryce Merriam.

“BU came out at us on the penalty kill, put our forwards in uncomfortable positions, and capitalized on it,’’ said RPI coach Seth Appert.

However, the hobgoblins that have haunted the Terriers quickly returned. After a sprawling pad stop by Merriam to prevent BU from doubling its lead, the Engineers tied the score when Brandon Pirri flipped a soft behind-the-net feed to Alex Angers-Goulet, who quickly buried it past Kieran Millan. Nineteen seconds later, RPI’s second shot of the night also found the back of the net. Defenseman Bryan Brutlag drove untouched down the right slot and slipped the puck between Millan’s pads.

Three minutes into the second period, BU knotted the score on a power-play marker. Zach Cohen deftly tipped a point blast from Nicastro over Merriam’s right shoulder. Seven minutes later, the Terriers regained the lead. With Eric Gryba in the box (becoming BU’s all-time penalty minutes leader in the process, surpassing Freddy Meyer), Shattenkirk rifled a wrist shot over Merriam’s glove.

With 10 minutes gone in the third, and BU facing a delayed call, Erik Burgdoerfer flicked a snap shot over Millan’s shoulder.

“We’ve been playing good hockey, but finding ways to lose games at critical points,’’ said Appert of his Engineers, who are 9-9-1 overall and 3-4 in ECAC Hockey. “Tonight, at critical moments, we had guys step up.’’

With six minutes left, RPI’s Christian Jensen got a loose puck from a scramble and shoved it into the net. Tyler Helfrich sealed it with an empty-net tally. The loss dropped BU to 4-9-3 and 2-7-2 in Hockey East.

“I don’t think there’s any question we need the break,’’ said Parker.