Selected first overall by the New York Mets in 1994, Wilson (5-7) allowed one run and six hits with one walk and four strikeouts. The righthander has been victorious in his last three decisions, pitching eight innings each time, after going winless in 12 straight starts since May 12.
Tampa Bay staged a two-out rally in the third inning, slapping four consecutive hits to open a 3-0 lead. Crawford got things going with a single before Aubrey Huff, Jared Sandberg and Steve Cox had RBI hits for the Devil Rays, who won for just the fifth time in 21 contests at Jacobs Field.
Conti added insurance for Tampa Bay, delivering an RBI single in the fifth before making the defensive play of the game in the seventh. He threw out Ricky Gutierrez, who was attempting to move from first to third on a single.
Esteban Yan yielded a solo home run to Milton Bradley before notching his 15th save.
Cleveland starter Danys Baez (8-9) surrendered four runs and eight hits in seven innings, walking three and striking out four.