With the Cardinals driving for a possible tying or go-ahead score with 1:04 remaining, Arizona quarterback Kevin Kolb lofted a pass that Chancellor picked off to preserve the Seahawks' three-point lead.
The Cardinals had one more chance in the final seconds but fell victim to the clock as they reached midfield, and Seattle (1-2) secured its first win of the season.
Two players who were with Minnesota last year had key roles in the Seahawks' win. Sidney Rice made eight grabs for 109 yards after missing Seattle's first two games with a shoulder injury, while Tarvaris Jackson completed 18-of-31 passes for 171 yards and an interception.
Kolb was 25-of-39 for 252 yards and a touchdown for the Cardinals (1-2).
Larry Fitzgerald made five catches for 64 yards and a score.