Murray's third score of the day capped a 12-play drive that was extended by a holding penalty on an incomplete pass on third down against cornerback Josh Shaw, the third time in the second half that Shaw was flagged for holding on third down.
Mariota finished 25 of 44 for 264 yards with an interception as Tennessee (6-3) won its fourth straight game.
Cincinnati (3-6) grabbed a 20-17 lead with 5:03 left when Andy Dalton hit A.J. Green with a short pass over the middle that Green turned into a 70-yard touchdown. Green broke a tackle near the Bengals 40 and raced into the end zone.
Tennessee opened the scoring with an impressive 84-yard drive on its first possession. Murray broke two tackles and tallied on a 2-yard touchdown run with 7:56 left in the first quarter.
The Bengals responded on Dalton's 37-yard scoring strike to Brandon LaFell, who was left wide open down the middle on a breakdown in coverage, with 4:44 remaining in the period. However, Randy Bullock hooked the extra point wide left.
Murray plunged over from the 1 with 5:08 left in the first half to make it 14-6. The score came one play after Cincinnati linebacker Vontaze Burfict, who was suspended for the season's first three games for repeated rules violations, was ejected for contacting a game official.
Joe Mixon punched it in on a 3-yard run with 1:42 left in the half, a play after Mariota was intercepted by cornerback Darqueze Dennard, to cut the Bengals' deficit to 14-13. But the Titans lashed together a drive capped by Ryan Succop's 44-yard field goal as time expired to give them a 17-13 halftime lead.
Dalton finished 20 of 35 for 265 yards, but lost a pair of fumbles in the second quarter, one leading to Murray's second touchdown.
NOTES: For the second straight game, Tennessee LG Quinton Spain (toe) was inactive and replaced by Brian Schwenke. ... Other inactives for the Titans were QB Brandon Weeden, WR Darius Jennings, CB Kalan Reed, DB Curtis Riley, LB Nate Palmer and DE David King. ... Cincinnati inactives were CB KeiVarae Russell, S Shawn Williams, LB Kevin Minter, G Alex Redmond, G Christian Westerman, WR Tyler Boyd and DT Pat Sims.