The clash got off to a pulsating start as Kenny Cooper fired the Sounders into a third-minute lead before Diego Chara leveled matters on 10 minutes.
The Timbers completed the turnaround just four minutes later when Diego Valeri struck to give Caleb Porter's men a 2-1 lead.
Former Fulham and Tottenham Hotspur ace Dempsey restored parity for the Sounders once more midway through the first half to ensure that the sides went in level at the interval.
However, the hosts emerged from the break much the better of the two sides and Chara bagged his brace within 10 minutes of the restart, while Maximiliano Urruti struck moments later to open up a two-goal lead.
Dempsey struck once more on 86 minutes to give Seattle a glimmer of hope, before the 31-year-old converted a penalty 100 seconds later to rescue a point for his side and deny Portland their first win this season.