The win kept the Patriots (8-5) locked in a three-team tie for the AFC East lead with the Miami and the New York Jets.
"It was a good win and now it looks like it's a three game season," said Patriots Coach Bill Belichick.
Cassel was 26-of-44 passing for 268 yards for the Pats while Welker notched a dozen catches for 134 yards.
Seneca Wallace completed 20-of-28 passed for 212 yards and three touchdowns to lead the Seahawks (2-11). Deion Branch caught two of Williams' scoring strikes and had a total of four receptions for 88 yards.
The Seahawks took a 21-13 lead late in the third quarter on a drive that featured a 63-yard reception by Wallace that gave Seattle a first-and-goal. Wallace made a juggling catch two plays later for the touchdown.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys