Boston University goaltender Jake Oettinger celebrated his 18th birthday less than a month ago. On Monday night at Boston College’s raucous Conte Forum, the second-youngest player in college hockey turned away every shot he faced to record a shutout in the Terriers’ 3-0 victory, their sixth straight win.

“That felt like playoff hockey out there tonight,’’ BU coach David Quinn said. “That’s not a surprise when our two teams meet, there’s usually a goalie pulled at the end and it comes down to a bounce here or there. We’re fortunate, but with that being said, I thought we played real well tonight.’’

Monday was the second installment of a cross-town home-and-home series between the teams. Playing at home on Friday, No. 5 BU (7-2-2 Hockey East, 14-5-2 overall) took the first game, 2-1, and Monday’s win marked the first time the Terriers have swept a home-and-home series with BC (9-3-1, 14-9-2) since 2002.

“I thought we skated a lot better tonight,’’ Quinn said. “We were more physical, and more physical in a disciplined way. We weren’t running around with our heads chopped off trying to kill people. We won small one-on-one battles and just played hard.’’

BU followed the lead of Oettinger, who recorded 34 saves and wasn’t fazed by the eighth-ranked Eagles’ three power plays. He consistently stood tall in the net while ignoring intense traffic in the crease. The shutout was Oettinger’s fourth of the season, moving him into a tie for the most in the country, and continues a stellar rookie season. The freshman is first in the conference in both save percentage (.937) and goals-against average (1.78) and is in the top 10 in both categories nationally.

“I think the difference was our defensemen,’’ Oettinger said. “They did a great job of making it easy on me, I don’t think I had to make any big grade-A saves. Me doing my job is just making simple saves and trying to be calm and be there for the guys.’’

The bloated final score hides what was a close contest for the vast majority of the game as well as an impressive performance from BC freshman goalie Joseph Woll, who recorded 29 saves. BU scored twice in the last minute of the game, including once on an empty-net, and all three goals came on the power play.

“Obviously he’s a great goaltender, he’s proved that the last two games, and it was kind of mano-a-mano,’’ said Oettinger, who played with Woll on the USA Hockey National Team Development Program the last two years. “It was really fun to compete against him because he’s such a great friend of mine, and when you know guys on the other team it’s a little more satisfying.’’

The deciding goal came with a power play winding down midway through the second period. Austin Cangelosi controlled possession near his goal and tried to scoot away from pressure by handling the puck himself. But Terrier freshman Kieffer Bellows skated up and poked the puck right to BU freshman forward Patrick Curry, who spun around and rifled a shot over Woll’s right shoulder with one second left on the power play.

The Terriers second goal, scored by sophomore forward Jakob Forsbacka Karlsson, came with 57 seconds left in the game and with two Eagles in the penalty box, and also was scored with one second left on the power play. Sophomore Bobo Carpenter finished out the scoring with a goal on an empty net.

BC spent the majority of the third period in BU’s zone but couldn’t get anything past Oettinger, who tallied 14 saves in the final stanza.

“The series was very well played by both teams, and I thought the goaltenders on both sides were maybe the stars of the weekend, making some really, really exceptional saves,’’ said BC coach Jerry York. “We played pretty well over the weekend, but pretty well is not going to win a big series. We’ve got to move up a level of play.’’

Everett Cook can be reached at evcook4@gmail.com. Follow him on Twitter @everettcook.