Arkansas first-year coach Chad Morris, who recruited and coached Deshaun Watson at Clemson, had high praise for Tagovailoa.
Ty Storey threw an 8-yard pass to Cheyenne O'Grady to put the Razorbacks on the board.
If you don't have speed then you're chasing speed, Morris said that day. Tagovailoa threw a short pass in the right flat to Smith, who broke free and went down the sideline, completing a 76-yard touchdown with only 21 seconds elapsed.
Tagovailoa connected with wide receiver Jerry Jeudy twice on passes of 42 and 60 yards for his last two scores of the afternoon.
The Crimson Tide also averaged 10.8 yards per offensive snap, crushing the previous high by an Arkansas opponent of 5.9 by Colorado State.
The only positive from Arkansas' defense came early in the second quarter when it stuffed Alabama on a fourth-and-one that set up the drive ending in Storey's fumble at the goal line. On the first, Arkansas cornerback Ryan Pulley stripped tight end Irv Smith after a 47-yard gain to the 12.
Arkansas had a chance to make things interesting in the second quarter after a Ty Storey touchdown pass was followed by a fourth down stop by the Razorbacks defense.
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Their time will surely come again - and when it does Liverpool's title aspirations will carry even greater weight. They didn't have one shot on target. "And Arsenal are two points behind and they won six games in a row".
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Tagovailoa has thrown one more touchdown pass (18) than Greg McElroy threw in Alabama's entire 2009 national championship season.
The Razorbacks have allowed a total of 72 points before scoring in the past four weeks, with deficits of 17-0 against North Texas, Auburn and Texas A&M, and 21-0 against Alabama.
Alabama had its way on the other side of the ball.
They didn't help that cause with three turnovers, with Alabama converting each of those into touchdowns, including a 44-yard interception return by Shyheim Carter with 12:15 left in the game, which gave the Tide a 58-17 advantage.
Not much has gone wrong for Alabama this season, but injuries on defense are beginning to pile up.
That's 30.4 yards per attempt, people.