McClellan rushed for a career-high 156 yards and two touchdowns and Burton caught a pair of scoring passes from Bryce Young during a 34-0 win over Austin Peay on Saturday.
The Crimson Tide (9-2, No. 8 CFP) took awhile to get going against Austin Peay (7-4) in a Bryant-Denny Stadium that wasn't much more than half full.
But McClellan and Burton had their biggest games for the Tide, which had already been knocked out of Southeastern Conference contention but was coming off a win over No. 14 Mississippi.
"All in all, we wanted to build on the momentum of how we came back and played at the end of last week's game," Alabama coach Nick Saban said. "And obviously I thought that's something we did a good job of today."
Burton posted his first 100-yard receiving game since transferring from Georgia, with seven catches for 128 yards. McClellan subbed for injured star Jahmyr Gibbs (ankle) and scored on runs of 1 and 9 yards.
McClellan, whose 2021 season was limited to five games because of injury, was coming off an 84-yard performance against the Rebels, when Gibbs went down.
"I've always thought he was a really good player," Saban said. "I think y'all are just starting to figure it out."
For much of the game the Tide was about as listless as the crowd, until a 50-yarder from Young to Burton provided a spark. McClellan rushed it in two plays later for his second score of the game, and the defense recovered a fumble on the next possession to set up an Alabama field goal.
The Governors had their opportunities in the first half thanks to the Tide's two first-quarter turnovers but could not take advantage either time, including a fourth-down stop in the red zone. Maddux Trujillo missed a short field goal for Austin Peay after Alabama's second fumble.
"We know that we competed with these guys," Governors coach Scotty Walden said. "If you watch the whole game, you saw a team compete to win. We didn't come here to keep it close. We came here to win the game."
Alabama got its second shutout of the season and first since an opening 55-0 win over Utah State.
Austin Peay: The FCS playoff hopefuls couldn't get much going offensively, but did well enough defensively to keep it from becoming an embarrassingly one-sided game.
Alabama: It wasn't the typical wire-to-wire domination for a Tide team against an FCS opponent, especially in the passing game. Alabama led just 7-0 more than halfway through the second quarter but wound up outgaining the Governors 527-206.
Alabama has struggled all year to force turnovers but had three against the Governors. Kool-Aid McKinstry and Brian Branch each had an interception, and Damon Payne Jr. recovered a fumble on a trick-play attempt.
"Three's our goal every single game, so to be able to reach that number was huge for us," Tide linebacker Henry To'oTo'o said.
Walden is hoping playoff selection committee members saw the whole game, not just the final score.
"If you're a committee member and you're watching that game, I don't know how you couldn't want us in," he said. "We've got the resumé for it. It's not just talk, it's the resumé."
Austin Peay hopes to receive an invite to the FCS playoffs.
Alabama hosts rival Auburn in the Iron Bowl.