Trailing by one point with 20 seconds to play, the Broncos opted to chase victory with a 64-yard field-goal attempt from Brandon McManus, rather than keep the ball in Wilson's hands. McManus' attempt, which would have tied for the second longest field goal in NFL history, had the distance but missed wide left.
Wilson, who was traded by the Seahawks to the Broncos in the offseason, completed 29-of-42 passes for 340 yards with one touchdown for Denver.
Smith was the star for the Seahawks, particularly in the first half, completing 23-of-28 attempts for 195 yards with two touchdowns. The Seahawks were scoreless in the second half but their defense held up.
Seattle scored a TD with their first drive as Smith found a wide-open Will Dissly, who had three receptions for 43 yards.
The Broncos tied it up in the second quarter when Wilson floated to Jerry Jeudy for a 67-yard to reception TD, which was his first in over 600 days. Seattle re-claimed the lead before half-time when Smith threw 25 yards to Colby Parkinson.
Denver came up empty on the goal line from Melvin Gordon and Javonte Williams in the third, before cutting the lead to one from a McManus field goal in the fourth, before his late career-long attempt missed. Wilson hit up Williams, before exhausting time and calling a timeout with 20 seconds remaining to allow McManus' attempt.
The win means Seattle have won their last eight Week 1 games at home, dating back to their last loss in 1999. Denver have lost six straight Monday Night Football games.