Coach Paul Johnson got the performance he wanted against an FCS opponent before the Yellow Jackets host Georgia next week.
Georgia Tech (7-4) used mostly third- and fourth-stringers in the second half as Johnson sought to keep top players healthy.
Jaymason Lee completed 14 of 27 passes for 205 yards and one touchdown for Alabama A&M (4-8). The Bulldogs ended the season by losing five of seven.
Georgia Tech announced that it set a modern-day school record for points in a single half and the most since 1950.
Quarterback Tim Byerly ran for a 20-yard score in the closing minutes to make it 66-7.
Alabama A&M scored late in the fourth quarter when Lee's 20-yard TD pass to Demario Ross cut the lead to 59-7.
Jackets linebacker Tyler Marcordes, making his first start of the season, had one interception, 1.5 sacks, three tackles and one forced fumble in the first half.
The sophomore's interception came against Terrance Pride on Alabama A&M's second play from scrimmage and set up the 6-yard run by Laskey that made it 14-0.
Marcordes replaced Brandon Watts, whose undisclosed injury snapped a string of 19 straight starts. Johnson said this week that Watts could return for the Georgia game, but added that he would not play against Alabama A&M.
Nealy's fumble return for a touchdown was the Jackets' first since Jerrard Tarrant ran one back against Mississippi State in 2009.
The Jackets, who attempted only six passes in the game, led 38-0 at the 10:52 mark of the second quarter. Sims' 39-yard touchdown run 4 minutes later gave them a 45-0 lead.
At that point, Georgia Tech had 315 total yards, 302 more than Alabama A&M.
Offensive tackle Ray Beno returned to the starting lineup for the first time since the Oct. 5 loss at Miami. Beno took 12 snaps at Clemson, but Johnson wanted him to play multiple series so he'll be ready for the Georgia game.
Connors added a 4-yard TD run early in the third to put Georgia Tech ahead 59-0.