Another victory will put the Orangemen into the "Sweet 16" in Albany, N.Y., which is just over two hours away from the Syracuse campus.
The Orangemen first took care of 14th-seeded Manhattan (23-7), a school with several ties to Syracuse.
"Manhattan is a very difficult team to play. They throw a lot of different defenses at you," Boeheim said. "I thought this was one of those games where you have to find a way to hang in there and survive. We did just that, survive."
The Jaspers cut the Syracuse lead to 39-38 on a three-pointer by Luis Flores with 16:53 left.
Syracuse responded with a 7-0 run on a dunk by Kueth Duany, a three-pointer by freshman Gerry McNamara and a layup by Hakim Warrick.
Jared Johnson had 22 points and Flores 18 for Manhattan, which appeared in the NCAA Tournament for the first time since 1995, when it stunned fourth seed Oklahoma in the first round.
"I thought we had a great run, I thought it was a special team," Gonzalez said. "I knew we wouldn't go away quietly. I thought we fought with everything that we had."
"We've been through a lot in four years," Johnson added. "Coach turned the program around."
Manhattan cut the lead to 61-56 with 6:57 left before the Orangemen quickly built it back to double digits on a jumper and two free throws by Anthony.
"We've been in that situation before where we've been up on teams and team have started to make a run," Anthony said. "We know that teams are going to make a run, regardless of who we're playing. We just have to keep our composure and keep playing the way we've been playing."
Dave Holmes had 10 rebounds for Manhattan, but the Orangemen still had a 35-21 edge on the boards.
"It was very difficult to score against them, which was exactly what I was worried about," Gonzalez said. We got outrebounded by 14. They're just a little too big for us on the boards."
Anthony had 10 of his points in the second half and Warrick, who was battling the flu, had all 10 of his points after intermission.
Edelin added 15 points off the bench for Syracuse, which used just eight players.
Syracuse led by as many as seven points on several occasions in the first half. The last came on a jumper by Josh Pace that made it 33-26 with 2:49 left.
A three-pointer by Minor and two free throws by Holmes cut Syracuse's halftime advantage to 35-31.