HEMPSTEAD, N.Y. — Ohio State punched through a program ceiling in Saturday’s NCAA quarterfinals. It doesn’t plan on stopping with a mere trip to Memorial Day weekend.

The third-seeded Buckeyes ripped Duke 16-11 at Shuart Stadium, sealing their first quarterfinal victory in four all-time tries. They’ll face either second-seeded Syracuse or unseeded Towson next Saturday in Foxborough, Mass.

“This was the hurdle we hadn’t gone over, and I think we all knew that without saying it,” coach Nick Myers said.

Eric Fannell had five goals and two assists, goalie Tom Carey made 14 saves and Jake Withers won 17 of 28 face-offs, as Ohio State (15-4) never trailed while controlling both ends of the field.

“It’s one of the best feelings I’ve ever had,” Fannell said. “Coming to Ohio State, I never expected anything less. It’s just a feeling of a lifetime. It’s special to be part of this and I don’t expect it to end without making more history.”

Jack Bruckner had three goals and an assist, and Justin Guterding added two goals and two assists for the Blue Devils (13-5), who had won their last nine quarterfinals.

Duke had not dropped a quarterfinal since 2002. It also hadn’t been this far in the tournament since its national title run three years ago.

“I thought our guys were tight,” Duke coach John Danowski said. “But that’s not disparaging to Ohio State. They were terrific.”

The Buckeyes showed no vulnerabilities at either end of the field. Fannell’s monster day was complemented by a deep supporting cast, and eight Buckeyes ultimately scored on the afternoon.

Ohio State offered a bit of a curveball, starting sophomore Jack Jasinski for only the third time all season. He delivered two goals and two assists, and his speed helped confound a Duke defense that hadn’t allowed more than 14 goals in a game all season.

Indeed, it was Lukas Buckley’s ability to run past his defender in the closing seconds of the first quarter — and the lack of any help coming from the rest of the Duke defense — that foreshadowed what was to come over the next 30 minutes.

“To me, that was the beginning of the light bulb going off for them to say, ‘Maybe we can run past these guys,’” Danowski said.

Ohio State didn’t let up. A 2-1 lead after a taut first quarter became a 9-4 advantage at the break. By the time the third quarter concluded, the Buckeyes led 13-5.

It was a welcome breakout for an offense that scored nine goals in a Big Ten title game loss to Maryland two weeks ago, then slogged through a 7-4 victory over Loyola in the first round of the NCAA tournament.

“We as an offense owed our defense one from last week, because they held us in there,” Fannell said.

Carey understandably drew attention for his 12 saves against the Greyhounds, and he made several sensational stops Saturday against Duke. His ability to smother Bruckner’s close-range shot in the early minutes of the third quarter made it clear the Buckeyes would not fade after sitting on a lead at the break.

But the defense playing in front of him was every bit as good. Bruckner and Joey Manown combined for just a shot in the first half while largely being defended by Matt Borges and Ben Randall, respectively, and Erik Evans helped contain Guterding for much of the day.

“We were fighting for another week, and we couldn’t be more excited that we got it,” Carey said.

While possession was an issue in the middle of the game for Duke, its offense made ill-advised choices when it did get the ball. That only made things easier for the Buckeyes.

“Our scout all week was to shoot low on him, and most of our goals that went in were low,” Guterding said. “Myself included, we were stubborn and shot high and wanted to blow it by him, and it didn’t work.”

Ultimately, though, it might not have altered the final result. Duke wasn’t at its best, but Ohio State was certainly close to accomplishing nearly everything it desired.

The Buckeyes had only five turnovers in the first three quarters, and they put 24 of their 31 shots on goal.

It was a distinctly different showing on this stage than the Buckeyes’ first three quarterfinal trips. They were drilled in 2008 (21-10 against Duke) and 2013 (16-6 against Cornell), then had a strong first quarter before Denver surged to a 15-13 victory in 2015.

There would be no deficit, no fade and no sputtering on Saturday.

“There’s being on a ride and being on a mission,” Myers said. “This team, from day one, has been so committed to the mission. I told them in practice this week it felt different from the last two times. Practice felt different, the attitude felt different, so that gave me a lot of confidence as a coach that we would come in here and put our best foot forward.”

It led the Buckeyes to their first final four, and few have Myers’ perspective on the accomplishment. He’s in his ninth year as a head coach, has been on staff since 2006 and understands exactly how far Ohio State has come.

He just isn’t quite ready to put into words what it means, not when at least one more game remains this season.

“There’s going to come a time where I’m more prepared to answer that question, but in fairness to these guys, I’m not ready to reflect,” Myers said. “I’m ready to make sure they get my very best tonight and tomorrow in preparation for next weekend. I’m not sure they would expect anything other than that from me, and I’m not going to expect anything different from them.”