Brady completed 35 of 53 passes for 337 yards and three touchdowns, his NFL-record 10th career playoff game with three or more TDs. Danny Amendola caught 11 passes for 112 yards for the Patriots.
Top-seeded New England will play in its seventh straight AFC title game next Sunday, hosting either the Pittsburgh Steelers or the Jacksonville Jaguars.
"It was a great team win overall," Patriots tight end Rob Gronkowski said on CBS. "On offense, everyone contributed. It was great. The wide receivers, running backs, tight ends. We all came in together and we worked together to get this win."
Quarterback Marcus Mariota finished 22 of 37 for 254 yards and two touchdowns and also led the Titans in rushing with 37 yards. Corey Davis made five grabs for 62 yards and two scores.
After beating the Kansas City Chiefs 22-21 in the wild-card round last week, Tennessee fell short of its first AFC title-game berth since 2002.
The Titans last beat the Patriots in 2002 and have not won in Foxborough since 1993, when the franchise played in Houston.
The Patriots had a playoff-franchise-record eight sacks in the game.
New England padded its 21-7 halftime lead and effectively sealed the result with Brandon Bolden's 2-yard touchdown rush with 4:02 remaining in the third quarter.
Brady's 4-yard TD pass to Gronkowski (six catches, 81 yards) made it 35-7 with 10:22 left in the fourth.
Brady shrugged off another thoughts that the Patriots were distracted by a bye-week ESPN report indicating a rift between himself, coach Bill Belichick and team owner Robert Kraft.
"You know what? No," he said of whether the report affected the team. "I've been around long enough, 18 years. There's so many nice things said about me. It just goes with the territory. I just try to be consistent. Show up and do the best I can do every week for the team. ...
"Being on the field, it's a great place. That's where you go prove it. You can talk all day about what you're going to do or what you can do. Ultimately, you have to go out there and do it. ... This team has done such a good job this year, focusing on what we need to."
Mariota connected with Davis for an 11-yard TD in garbage time with 1:55 to play.
"We have to use this as motivation," Mariota said of the defeat, according to WKRN.com of Nashville. "You can't hurt yourself. It's tough to get in a hole and dig yourself out."
Tennessee led 7-0 after Davis' one-handed touchdown grab on a 15-yard pass from Mariota capped a 95-yard drive with 1:14 left in the first quarter. It was Davis' first career NFL touchdown catch.
After a 50-yard TD pass from Brady to Dion Lewis was negated when Lewis was ruled down at the Tennessee 19, the Patriots tied the game on Brady's 5-yard shovel pass to James White at 13:18 of the second.
White's 6-yard TD run with 9:20 to go in the half gave the Pats their first lead at 14-7. Brady tossed his second TD to Chris Hogan from 4 yards out with 1:52 to play before the break.
--Field Level Media