It nearly marks the most points scored by an SEC opponent since Ole Miss barely lost to the Tide 48-43 in September 2016.
Tagovailoa completed his first three passes, two for touchdowns, before Kamren Curl made a diving breakup in the end zone on a pass intended for Irv Smith.
Ty Storey threw an 8-yard pass to Cheyenne O'Grady to put the Razorbacks on the board.
You say you're the best fans in college football, you need to show up. The Tide marched 99 yards to go up 28-14 when Jerry Jeudy hauled in a Tagovailoa pass and raced 42 yards for the score. We're obviously doing that better on offense than on defense. Their last nine opponents averaged only 5.1 first-half points.
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 came into Saturday having not been tested all season long and that trend continued against Arkansas.
Once again, Tagovailoa connected with Smith for a huge gain near the Arkansas 20 before cornerback Ryan Pulley forced a fumble. He is now 76-of-102 for 1,495 yards and has no interceptions on the year, and he has yet to play in a fourth quarter.
Tagovailoa has thrown one more touchdown pass (18) than Greg McElroy threw in Alabama's entire 2009 national championship season. De'Vion Warren's nice sliding 17-yard touchdown reception from Storey came against backups in the fourth quarter and Kelley added a one-yard touchdown run to cover the 35-point spread.
Tua Tagovailoa's had another big day at quarterback as the Tide's starter went 10-of-13 passing for 334 yards and four touchdowns.
Alabama had its way on the other side of the ball.
Alabama entered the game ranked No. 1 and did nothing to relinquish that position. Alabama is also with freshman defensive back Jalyn Armour-Davis, who suffered a season-ending knee injury last month.
Connor Limpert made a 41-yard field goal and is now 8-for-11 in field goal attempts.