However, the Cowboys restored parity just before the end of the first quarter when Tony Romo handed the ball to DeMarco Murray on the third to go behind a block of Kyle Bosworth and run in for a touchdown.
The Raiders, though, rallied in the second quarter and surged ahead with 10:13 left before half time, Rashad Jennings with the touchdown after sweeping to the right before running across the field and sprinting in.
Then with just under two minutes left before the interval, Jennings scored his second touchdown of Thanksgiving Day by powering to the endzone after taking the handoff on the one-yard line.
The Cowboys gave themselves a fighting chance on the stroke of half time thanks to a touchdown from Murray, and they dug deep in the third quarter.
It was level pegging 10 minutes in when Romo picked out Dez Bryant with a neat pass, allowing his teammate to claim his ninth receiving touchdown of the season.
Murray powered through into the endzone for the seven-yard score early in the fourth quarter to make it 27-21 to the Cowboys before Dan Bailey added a field goal to give them breathing space.
Sebastian Janikowski hit a 45-yard field goal at the other end with 35 seconds left on the clock, but it proved little more than consolation for Oakland.