Tampa Bay (5-7) slipped three games behind Dallas and Carolina in the race for the two NFC wild card berths with four games remaining.
Leftwich, a rookie who had thrown eight touchdowns and 12 interceptions entering the contest, went 20-of-34 for 224 yards and two TDs without an interception for Jacksonville (3-9), which entered the contest tied with Atlanta and San Diego for the worst record in the NFL.
The game was tied, 10-10, before Leftwich connected with Smith down the right sideline for the go-ahead score with 10:23 left. Smith made a diving catch past Bucs corner Tim Wansley.
Fred Taylor had 29 carries for 119 yards and Smith 10 catches for 136 yards for Jacksonville.