UCLA maintained an eight-point lead at halftime, entering the locker room at the break ahead 47-39.
The Bruins will face No. 6-seed Cincinnati (30-5) in a second-round matchup on Sunday, March 19.
''If you lose, you're done until next year, so that makes it a lot more pressure on you,'' Leaf said.
Kent State (22-14) received 20 points and a team-leading 15 rebounds from senior Jimmy Hall, who made 9 of 18 shots from the field in 31 minutes. The Golden Flashes had entered the NCAA Tournament after having defeated the top three seeds in the Mid-American Conference Tournament last week.
Jaylin Walker finished with a team-leading 23 points for Kent State.
''Couldn't be more proud of our guys in terms of how we fought the entire game and during the season we had this year,'' Kent State head coach Rob Senderoff said.
The Golden Flashes reduced UCLA's lead to as few as five points midway through the second half. Walker's layup with 17:03 to play in regulation cut the Bruins' margin to 52-47. Less than a minute later, Walker nailed a three-pointer to close the gap to 54-40.
From that point, UCLA used a 9-3 scoring run to lead 63-53 at the 12:20 mark. A layup by Holiday with 7:31 left in the second half put the Bruins ahead by 10 points and UCLA's advantage never fell to single digits.
With Friday night's win at the Golden 1 Center in Sacramento, Calif., UCLA improved to 5-2 in three NCAA Tournament trips under fourth-year head coach Steve Alford.
UCLA's game on Sunday evening against No. 6-seed Cincinnati will be nationally televised on TBS. The Bruins' game will be available on the radio in the Los Angeles area on AM 570 (KLAC).
Prior to UCLA's game at the Golden 1 Center, No. 3-seed Oregon will face No. 11-seed Rhode Island in a second-round matchup (Midwest Regional). That game is slated to begin at 4:10 p.m. (PT).