The Seahawks trailed 23-10 in the fourth quarter, but began a comeback when Wilson connected with Braylon Edwards on 10-yard scoring strike with 7:26 to go, cutting the deficit to six points.
After stopping two New England drives, Seattle (4-2) grabbed the lead when Wilson got the ball at his own 43-yard line and launched a long third-down pass that found Rice in the end zone.
Wilson finished 16-of-27 for 293 yards and three scores for the Seahawks, who improved to 4-0 at loud CenturyLink Field.
Tom Brady connected on 36-of-58 passes for 395 yards and two touchdowns with two interceptions for the Patriots (3-3).
Wes Welker made 10 grabs for 138 yards and a score for New England.