ATLANTA — Jameis Winston threw for four touchdown passes and the Bucs made a promising start to the Dirk Koetter era, pulling out a 31-24 win over the Falcons at the Georgia Dome.The Bucs (1-0) got four touchdown drives of 75 yards or longer in a span of five possessions, getting a win for Koetter and defensive coordinator Mike Smith, who both coached in Atlanta (0-1) before joining the Bucs. With a tough month ahead -- including a Week 2 game at Arizona — it's a crucial early win for the Bucs, who beat the Falcons for the third straight time. Tampa Bay saw an 18-point lead cut to seven with five minutes to play. Their offense got two key first downs to run the clock down inside the two-minute warning. The Bucs' defense clinched the win when Gerald McCoy tipped a Matt Ryan pass on fourth down.Tampa Bay trailed 10-3 early as an early Winston interception set up a Falcons touchdown. But Winston collected himself and went 6-for-6 with a touchdown to tight end Brandon Myers to tie the game.Down 13-10 with 1:45 left in the first half, Winston marched the Bucs on another scoring drive, with Charles Sims twisting through defenders for a touchdown and a 17-13 halftime lead.Winston would throw touchdowns on his first two drives of the third quarter, with strong catches by tight end Austin Seferian-Jenkins (30 yards) and receiver Mike Evans (45 yards) for a 31-13 lead.Atlanta would answer, however, going for it on fourth-and-3 at midfield, then getting a 25-yard touchdown pass to Julio Jones and two-point conversion to cut the lead to 31-21.