The Monmouth players tried to establish themselves with a strong physical presence early, notching six fouls in the first 4:14 of the game.
Notre Dame forward Scott Martin said they just didn't have the size to maintain that style of play.
"They were trying to throw their weight around," Martin said. "Unfortunately for them, we were a little bigger and stronger than them."
Dion Nesmith led the Hawks with 13 points, followed by Andrew Nicholas with nine.
First-year Monmouth coach King Rice praised the Irish for their teamwork, something he wants his own team to emulate.
"They're a really good program, and hopefully someday we can get better and at least be able to give them a game," Rice said. "They play the right way; they share the ball. You can just see they're a team, and that's what we're trying to build."
Garrick Sherman had a career-high 22 points and seven rebounds to lead the Irish. Jack Cooley added 16 points for the Irish (2-0) and Pat Connaughton had 13.
"I take my hat off to Coach (Mike) Brey and the Notre Dame team," Rice said. "I recruited a bunch of kids on the Notre Dame team when I was at Vanderbilt, and he does a great job, the type of kids he gets. I take my hat off to those kids, man, because they really know how to play basketball."
As Sherman came off the court with the game well in hand, he said the same thing to everyone he high-fived on the bench: "It's about time."
The Michigan State transfer said he was "embarrassed" by his 3-point performance Saturday in the season opener against Evansville, and was determined to come out more aggressive against Monmouth.
"I think I was a little too passive in the first game, trying to find my role," the 6-foot-10 senior forward said. "I owe it to Coach Brey and I owe it to this program to start playing better."
Monmouth (1-1) scored the game's first four points, but Cooley's free throw 4 minutes into the game put the Irish ahead for good. Notre Dame stretched its lead to 17 points with 1:31 to go in the first half, before Monmouth's Nicholas cut the deficit to 12 with a 3-pointer at the buzzer.
Notre Dame, which out-rebounded Monmouth 42-24, shot 61 percent from the free throw line.
Nesmith led the Hawks with 13 points.
Brey said it was the first time he had been able to play Cooley and Sherman together for long stretches.
"That really helped us, just being able to pound away with two big guys," Brey said. "This is so important for (Sherman) as we head to Brooklyn. That's a game that kind of makes him believe he's really part of it."
Brey said Sherman has the footwork and agility to play very "crafty," so it's been a challenge to slow down his game.
"We did a good job feeding him," Brey said. "He has the best feel of our big guys to present himself as a receiver in a good spot. "
The Irish travel this weekend to the $1 billion Barclay's Center in Brooklyn for the championship rounds of the Coaches vs. Cancer Classic. Notre Dame will play Saint Joseph's on Saturday, then either Florida State or BYU on Sunday.
Monmouth was outscored 40-20 in the paint, and hit only 2 of 11 from 3-point range. The Irish were 6 of 21 on 3-pointers, with Connaughton hitting three.
The Irish again were lackluster from the free throw line, hitting just 16 of 26 -- a slight improvement from the 18-of-30 effort in their season opener Saturday against Evansville.
Monmouth shot just 39 percent from the field, compared to 53 percent by the Irish.
Monmouth turned the ball over 18 times to Notre Dame's 16, but the Irish turned those into 28 points, while Monmouth converted the Irish turnovers into just 10 points.