The Cowboys, still looking for their first win since Tony Romo's broken collarbone in week two, were the first to get into the opposition redzone as stand-in quarterback Matt Cassel survived a fumble and a sack to take his side downfield.
However, the sack ensured that Tampa Bay would limit the damage, with Bailey's 42-yard kick giving the visitors a three-point lead.
They weren't level for long, however, although it took another field goal of more than 50 yards, this time from Bailey, to nudge the Cowboys back in front.
Both kickers missed a chance to add to the score with wide field goals in the second quarter, Barth skewing his to the left from 46 yards and Bailey sending his wide right from 48 yards.
The Cowboys were handed another opening before the half was out when Winston's pass to Brandon Myers was intercepted by Jeff Heath, but they were unable to make the most of it and the gap remained three going into the break.