Tatum hit 6 of 9 shots from the field, including back-to-back 3-pointers that helped break the game open early in the second half.
Scotty Hopson nailed 4 of 6 shots from beyond the arc and led the Vols with 16 points. Fellow sophomore Tatum chipped in 15. Tyler Smith (14 points, 11 rebounds) and fellow senior Wayne Chism (11 points, 10 rebounds) contributed double-doubles.
Tennessee's superior depth and quick tempo proved decisive as it outscored AP 52-29 in the second half and 38-10 in bench points. The Vols had the Governors gasping for breath in the game's final minutes.
Tennessee forced 19 turnovers, outshot the visitors 49 percent to 34 percent from the field and outrebounded the Governors 46-33.
"I thought we showed really good knowledge defensively," Pearl said on his post-game show. "I think we're a little smarter defensively. I think the guys understand how to guard and how to help one another. I was pleased with our effort defensively, with the exception of the last four minutes of the first half."
Tennessee came out smoking, forcing three Governor turnovers en route to a 7-0 lead. After Austin Peay closed to 12-10, the Vols went on a 15-0 run to go up 27-10. Hopson hit a couple of 3-pointers during the outburst.
The Governors switched to a 2-3 zone at this point, however, and Tennessee's offense slowed to a crawl. The Vols were outscored 15-4 over the half's final 8 minutes and went to the break leading just 31-25.
"It slowed us down," Pearl said of the zone. "I've not spent a lot of time with zone yet.... We could've shot 'em out of it but we missed some open shots against the zone.... We didn't hit those shots, so they stayed in it and it did slow us down.
"You can continue to run your fast break against zone. Our guys just don't know how to do it yet."
Tennessee regained the momentum at the start of the second half, thanks to a 9-0 spurt. Smith scored 8 of the 9 - hitting a scoop shot, a coast-to-coast dunk, a tip-in and a garbage bucket - as the lead swelled to 40-25.
"Tyler Smith looked like an NBA player tonight, when he was climbing the boards," Pearl said. "He was the best athlete on the floor, and they (Governors) have some nice athletes.... He played with great energy tonight."
Following Smith's one-man spurt, Tatum drained his back-to-back 3s and Hopson scored on a transition dunk. Brian Williams added a three-point play, then Hopson drained a 3. Suddenly, the lead was 54-32 with 11:54 to go.
The Vol lead peaked at 83-52 on back-to-back 3-pointers by walk-on Michael Hubert.
Anthony Campbell scored 17 points to pace Austin Peay.
"I was pleased with our effort overall," Pearl said. "To win by that margin and have a couple of key players (J. P. Prince, Bobby Maze) really have off nights is a good sign."
Although Pearl emptied his bench in the final minutes, Renaldo Woolridge, a 6-9 scholarship sophomore, did not play in the game. That raises the possibility that he might redshirt this year.
Tennessee returns to action Tuesday at 7, hosting UNC Asheville.