It got better as the Broncos went on to win 48-21.
"We played all right, not spectacular," Moore said after his 46th win, one more than former Texas quarterback Colt McCoy.
Broncos coach Chris Petersen said his team would have to do better against next week to beat TCU.
"That's news to me that we threw five touchdowns. We were not clicking," he said.
Moore threw two touchdowns each to Tyler Shoemaker and Matt Miller, racking up 224 yards through the air on 18-of-31 passing despite leaving the game early in the fourth quarter.
"It's great. Kellen is a winner," Petersen said. "A lot of guys around here are winners."
UNLV (2-6, 1-2 Mountain West Conference) matched the Broncos' first two touchdowns, but a pass interference call close to halftime set up Boise State's go-ahead score.
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Moore, in his fourth year as the Broncos starting quarterback, is 46-2, tops among FBS quarterbacks in career winning percentage (95.8 percent). Stanford's Andrew Luck is second at 85.3 percent (29-5).
"You have a lot of respect for those guys on that list," Moore said. "I'm very fortunate. I'm very fortunate to play at Boise State."
Boise State (8-0, 3-0) pulled away from UNLV during the second half, as Moore found Shoemaker streaking past UNLV's secondary in the middle of the field for a 51-yard touchdown with 8:37 left in the third quarter.
On its next possession, the Broncos faked a punt on fourth-and-8, snapping the ball to J.C. Percy and letting him run 20 yards before he was tackled at the UNLV 31-yard line.
Shoemaker then gave Moore his fifth touchdown, as the fourth quarter began, when he caught a ball that had been deflected in the end zone by a UNLV defender.
DJ Harper and Drew Wright added rushing touchdowns for the Broncos in the fourth quarter.
During the first half, the Broncos looked nothing like the 41-point favorites Las Vegas casinos thought they were. Two of their three first-half touchdowns were set up by UNLV mistakes.
Early in the second quarter, Boise State blocked a punt and took over needing 40 yards to score. Less than two minutes later, Moore hit Miller for a 30-yard touchdown.
Just before halftime, UNLV was called for pass interference and penalized 15 yards, setting up first-and-goal for the Broncos with just over a minute left. Three plays later, Moore found Miller again for a 5-yard score.
At the break, each team had run 32 offensive plays, but UNLV had 198 yards compared with 161 for Boise State.
UNLV coach Bobby Hauck said he was happier with his team's play in the first half, but it still missed opportunities.
"Certainly [Boise State is] a pretty good football team, and we struggled to keep up in the second half," he said.
The matchup was the first between the teams since the 1970s, and could be their last for a while if Boise State leaves the Mountain West after one year for the Big East Conference.
Athletic department spokesman Max Corbet told the Associated Press before Saturday's game that the school hadn't received a formal invitation from the Big East and hadn't decided the future of its program. He said the school wouldn't be immediately prepared to accept an invite without considering what is best for all its sports.