Unga ran for three touchdowns and 149 yards, and Hall completed 21 of 27 passes for 320 yards and two more scores in BYU's 59-21 victory. The Cougars (5-1, 2-0 Mountain West) gained 611 yards and led by double digits for the final 48 minutes.
"I thought the team played well and played a complete game," BYU coach Bronco Mendenhall said. "We improved in a lot of areas.
UNLV coach Mike Sanford fell to 13-40 in five seasons with the Rebels (2-4, 0-2).
"First thing is to give BYU credit," Sanford said. "They are a very good football team. They are the 18th-ranked football team in the country and played like it."
Hall's 35-yard touchdown pass to Dennis Pitta put the Cougars back up by 17 and the Rebels weren't a threat again. BYU added a 1-yard run from Jo Jo Pili and a 15-yard touchdown pass to JJ Di Luigi for a 45-14 lead at the end of the quarter.
"Max is the cornerstone of this team and this offense," Unga said. "Hes a great leader. He is one of those quality guys who can lead team during crunch time."
Unga scored all three of his touchdowns in the first 20 minutes, breaking free for a 52-yard run with 11:12 to play in the second quarter to give BYU a 24-7 lead.
Unga also ran it in from 33 yards and 1 yard and Mitch Payne added a 28-yard field goal.
"[Unga] is a different type of ball player. He makes everything look easy," Mendenhall said.
BYU, which entered averaging 34 points and 432 yards per game, took advantage of a UNLV defense that surrendered 773 yards last week in a 63-28 loss at Nevada.
The consecutive poor performances could cost Sanford his job. He spent parts of his postgame media conference answering questions about his future.
"Coach Sanford will make sure all of our focus is on the next game," Clayton said. "Those other things are out of our control."
The Cougars have scored 136 points to win their three games since a 54-28 loss to Florida State on Sept. 19.
Unga is still upset about that loss.
"Florida State is a real great team and they beat us by playing their game," Unga said. "I just wish we could play them again."
A 94-yard kickoff return for a touchdown by Deante' Purvis gave the Rebels their only points in the first half. It was UNLV's first kickoff return for a touchdown since 1999.