Mariota threw four touchdown passes in the first half Sunday as the Titans raced to a 35-7 halftime lead over Winston and the Buccaneers in a game featuring the top two picks in this year's NFL draft.
The Titans already have surpassed their highest point total from last season, when they went 2-14 before drafting Mariota with the No. 2 overall pick.
Mariota, who won the Heisman Trophy last year while at Oregon, completed 10 of 13 passes for 175 yards in the first half. He is the first player in league history to throw two touchdown passes in the first quarter of his NFL debut, according to the Elias Sports Bureau.
While Mariota was impressive early, Winston's career started in inauspicious fashion. The 2013 Heisman winner threw an interception to Coty Sensabaugh, who returned it 26 yards for a touchdown, on his first passing attempt and was intercepted on a screen pass in the second quarter as well.
Mariota orchestrated an 89-yard drive on Tennessee's opening possession, punctuated by a 52-yard touchdown pass to Kendall Wright. He also threw touchdown passes to Bishop Sankey, Harry Douglas and Delanie Walker.
Winston got the Buccaneers on the board on the first play of the second quarter, when he found Austin Seferian-Jenkins for a 5-yard touchdown that made it 21-7. The No. 1 overall pick completed 6 of 12 passes for 70 yards in the first half.
ESPN Titans reporter Paul Kuharsky and ESPN.com's Jeremy Fowler contributed to this report.