New Seahawks quarterback Geno Smith looked comfortable in Wilson's old position, throwing for two touchdowns and 195 yards.
Wilson did his best to keep the Broncos hopes alive, picking up 340 yards in the air, but was only able to find the end zone once.
The Seahawks got off to the best possible start, with Smith finding Will Dissly on a 38-yard touchdown reception on the first drive of the game.
Both teams then traded field goals before Wilson got his first and only touchdown of the game through wide receiver Jerry Jeudy.
Seattle responded immediately with Colby Parkinson's 25-yard touchdown reception to give the home side a boost headed into the second half.
Both offences stalled in the third quarter, until a field goal at the start of the fourth brought the visitors to within a point.
However, kicker Brandon McManus missed a 64-yard field goal attempt in the dying seconds to ultimately seal the narrow victory for Seattle.