The Patriots' streak, which includes playoff triumphs, is the longest in NFL history. They tied the league's regular-season record with their 17th straight win.
Brady completed 19 of 30 passes in helping the Patriots to a 5-0 record for the second time in franchise history.
Seattle's only touchdown came from Shaun Alexander and briefly moved the Seahawks within three points in the fourth quarter. Josh Brown added four field goals for Seattle, which fell to 3-2 with its second straight loss.
New England's first two scores, a touchdown and field goal, were set up by interceptions from Willie McGinest and Ty Law.
The Patriots took a 17-0 lead early in the second quarter on a six-yard throw from Brady to David Patten.