Their three losses this month all close, two by four points before falling by a touchdown against the Cowboys (7-5).
"We just need to learn how to finish," said cornerback Mike Jenkins, like Burnett a former Dallas player.
Dallas was without kick returner Dwayne Harris because of a hamstring injury, and rookie replacement Terrance Williams gave the Raiders a touchdown with a fumble on the opening kickoff. Greg Jenkins picked up the ball at the 23 after it squirted away from the pile and outran everyone to the pylon.
The play was upheld on review after replay showed Williams' knee hitting the turf just as the ball was coming out.
Matt McGloin had a strong first half for the Raiders, leading consecutive TD drives for a 21-7 lead. But he didn't get much help from the league's fifth-best rushing attack, and his offense stalled in the second half.
"We started out fast, we just couldn't hold up," Raiders coach Dennis Allen said. "The momentum changed there at the end of the first half when they were able to get down the field and get the touchdown there at the end of the first half. (After that), they were able to possess the ball, so therefore we didn't have many opportunities on offense to get much going. And when we did, we weren't really able to take advantage of it."
Rashad Jennings rushed for 35 yards on 17 carries — a 2.1-yard average — and had both of Oakland's offensive touchdowns. Darren McFadden carried just five times for 13 yards in his return after missing three games with a hamstring injury.
McGloin converted five straight third downs with passes on a pair of touchdown drives in the second quarter. He also had a throw to Holmes that was ruled a touchdown on second-and-goal from the 16. After the call was overturned on replay, Jennings scored from the 1 to put Oakland ahead 14-7.
Jennings had another 1-yard scoring with 1:56 left before halftime, but the Cowboys had time to get a 4-yard TD from Murray with 10 seconds left.
Murray ran 17 times for 63 yards while Lance Dunbar had 82 yards on 12 carries for Dallas.
McGloin, an undrafted rookie out of Penn State, was making his third career start, two weeks after beating Houston in his debut as a starter. He was 18 of 30 for 255 yards with an interception.
"I don't know if he played as well as he did in some of the previous weeks, but I still thought he did some good things. I still thought he was able to throw the football, we were able to get the ball down the field some," Allen said. "A couple of mistakes in the game, but I wouldn't say it was a poor performance."
Soon after a 35-yard pass to Andre Holmes with the Raiders at the Dallas 20 with just under 9 minutes left, McGloin threw a ball to the back right corner of the end zone toward Jacoby Ford. Brandon Carr leaped as well, and picked off the pass.