Moments before Dallas scored in the 18th minute, Dempsey had a penalty shout denied by the referee, but they worked hard to get back on level terms, with Erik Friberg and Tyrone Mears having chances at goal.
The home side finally found the breakthrough after the half-time interval when Andreas Ivanschitz thumped the ball into the back of Jesse Gonzalez's net in the 67th minute after surging through Dallas's defence.
The game had a quiet spell with neither side forcing through a winner, but with just four minutes of normal time remaining, Dempsey stepped up to take a crucial lead in the semi-final tie.
Cristian Roldan conceded a free kick just outside of the box, and Dempsey, who has previously played for Fulham and Tottenham Hotspur, managed to send the ball past the keeper to take a 2-1 win for Seattle.
The Sounders will grab a spot in the final if they win or draw the second leg in Texas on Sunday.