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A short pass to Brian Quick resulted in a second score for the Rams as the wide receiver sprinted after the catch to the endzone.
DeMarco Murray kept the visitors in contention at the break though, running in just before the end of the second quarter.
The Cowboys comeback continued in the second half as Romo completed a deep pass to Bryant to give the wide receiver his second touchdown of the season, while Dan Bailey kicked his second field goal of the game to leave Dallas just a point down.
The Dallas comeback continued in the fourth as Terrance Williams held on to a long throw from Romo before Bruce Carter intercepted Davis before running it back for another six points, giving the NFC East side a 10-point advantage.
Austin Pettis got the scores close again late on as Davis threw the ball out wide for the receiver, but a late interception as the Rams were pushing to get back ahead late on ensured that the Cowboys held on for the win.