Quarterback Jameis Winston of the Tampa Bay Buccaneers passes the...

Quarterback Jameis Winston of the Tampa Bay Buccaneers passes the ball in the second quarter against the Atlanta Falcons at Raymond James Stadium on Dec. 6, 2015 in Tampa, Fla. Credit: Getty Images / Cliff McBride

TAMPA, Fla. — Jameis Winston is determined to help the Tampa Bay Buccaneers become relevant any way that he can.

The No. 1 overall pick in this year’s draft threw a 6-yard touchdown pass to Mike Evans with 1:39 remaining, giving the surging Bucs a 23-19 victory over the Atlanta Falcons on Sunday.

Winston also scored on a 5-yard run and scrambled up the middle of the field 20 yards on third-and-19 to extend the third game-winning drive of his young career.

Lavonte David sealed the fourth victory in six games for the Bucs (6-6), intercepting Matt Ryan’s pass intended for Julio Jones on Atlanta’s final possession. The Falcons (6-6) have lost five straight, six of seven overall, after starting the season 5-0.

Winston completed 18 of 27 passes for 227 yards, one touchdown and one interception.

But it was his timely run and ability to make another 10 yards after appearing to be stopped at the Atlanta 33 that typified what the 2013 Heisman Trophy winner has meant to Tampa Bay, which has overcome a slow start to contend for a playoff berth.

Doug Martin rushed for 95 yards and one TD for Tampa Bay, which drove 80 yards in 12 plays to take the lead for good. Evans finished with five receptions for 61 yards.

Ryan was 30 of 45 for 269 yards, including a 5-yard TD throw to Nick Williams that put the Falcons up 19-16 early in the fourth quarter. His late interception was Atlanta’s only turnover of the game.

Shayne Graham kicked four field goals, two of them in the final 1:01 of the opening half to give the Falcons a 9-6 lead. The Bucs contributed to the quick turnaround by trying to move the ball instead of running out the clock and settling for a one-point halftime lead.

Winston, who also led a game-winning drive in overtime to beat the Falcons in Atlanta on Nov. 1, completed two passes before a throw intended for Evans glanced off the receiver’s hands and was intercepted by Desmond Trufant at the Falcons 49.

Ryan used a pair of short completions to Jones to position Graham for a 52-yard field goal on the last play of the half. A 29-yarder on the opening possession of the third quarter expanded Atlanta’s lead to 12-7.

Jones had eight catches for 93 yards, going over 100 receptions in a season for the second straight year. The league’s receiving leader has 102 for 1,338 yards through 12 games.

The Bucs played without three-time Pro Bowl defensive tackle Gerald McCoy, who sat out after injuring his left hand injury during the previous week’s 25-12 loss at Indianapolis.

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