Gradkowski started 11 games with Tampa Bay in 2006 and one with Cleveland last season and hopes to challenge former No. 1 draft choice JaMarcus Russell for the top spot with the Raiders.
With Dallas owning a 10-7 lead early in the second quarter, Gradkowski drove Oakland 62 yards in five plays and the Raiders took the lead for good on a 3-yard pass to Tony Stewart.
Gradkowski also put together drives of 80 and 69 yards in the third period -- marches that ended with touchdown runs of 3 yards by Louis Rankin and 1 yard by Gary Russell.
JaMarcus Russell completed 6-of-9 passes for 50 yards in one quarter of work.
Dallas quarterback Tony Romo played for only two series, but on the second one he drove the Cowboys 71 yards in nine plays and threw an 8-yard touchdown pass to Jason Witten.
Since appearing in the Super Bowl at the end of the 2002 season, Oakland has had six straight losing campaigns -- the longest stretch of losing seasons ever by a team after earning a Super Bowl berth.