The Jaguars were trailing 13-9 when McCown hit John Matthews for the decisive 27-yard score in the fourth quarter.
David Garrard completed 24-of-31 passes for 211 yards for Jacksonville, now 1-2.
Earnest Graham got the Bucs' only touchdown on a 2-yard catch in a game that was held up for 35 minutes late in the first quarter because of lightning.
Connor Barth booted two field goals for Tampa Bay.
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