The Crimson Tide (10-1, No. 2 CFP) led 49-0 by halftime against the Buccaneers (9-2), who are bound for the FCS playoffs. Alabama is hoping to join them in the FBS version and can clinch an SEC West title with a win next week at Auburn.
Jones scored on returns of 43 and 72 yards. He's the only Alabama player to score twice on punt returns, according to school records dating to 1944. He's also the first Tide player to have touchdowns on punt returns in consecutive games.
Henry tied Trent Richardson's Alabama single-season record of 21 touchdowns before sitting out the second half. He had nine carries for 68 yards.
The few remaining fans gave a big cheer in the final minutes after No. 9 Michigan State upset No. 2 Ohio State. The Buckeyes knocked Alabama from the playoffs last season en route to a national title.
This game had no such drama, as expected. The 49 first-half points were the most for the Tide under coach Nick Saban.
The starters posted good numbers before giving way to the backups for much of the game.
Jake Coker completed 11 of 13 passes for 155 yards with a 30-yard touchdown to Calvin Ridley and a 21-yarder to Richard Mullaney before heading to the sidelines. Henry scored on runs of 17 and 2 and has touchdowns in 16 consecutive games.
Freshmen Damien Harris and Bo Scarbrough added short touchdown runs. Alabama had eight players run the ball and 10 catch passes from three different quarterbacks.
Alabama outgained the Buccaneers 403-134.
Copeland was 3 of 7 passing for 46 yards and ran 15 times for 25 yards. Leading rusher Darius Hammond didn't have a carry.
This game was clearly a mismatch from the outset, with Alabama at one point gaining 154 yards while Charleston Southern had minus-7.
The Tide still managed to turn in highlight reel plays even with little drama in the game, beyond Jones' scampers. Among the 25 seniors playing their final game at Bryant-Denny Stadium, Jones batted a pitch down in Charleston Southern's backfield and nearly scored again right after his second TD, making it to the 6.
Jones also ran back a punt last week against Mississippi State.
Richard Mullaney made it 21-0 with a leaping grab in the back of the end zone 13 minutes into the game. Replay reversed the initial call, determining he had possession when he managed to stick his left foot down in bounds while falling backward.