Romo went 25-of-39 through the air with an interception while DeMarco Murray compiled 38 yards on 18 carries in the defensive struggle.
Miles Austin led the Dallas receiving corps with five catches for 107 yards as the Cowboys (2-1) rebounded from a 27-7 loss to Seattle last week.
The Buccaneers (1-2) were stymied by Dallas' coverage against Josh Freeman, who managed to complete just 10-of-28 passes for 110 yards with a touchdown and an interception.
Doug Martin paced the Bucs with 53 rushing yards on 19 carries.
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