Andres Escobar drew the penalty on Seattle midfielder Marco Pappa's careless challenge.
Pappa redeemed himself with a free kick that set up Alonso's tying goal. Pappa's placement kept goalkeeper Raul Fernandez on his line and gave Alonso the room to head it in.
Fabian Castillo nearly put Dallas in front in the 90th minute with a 40-yard run and blast that Frei deflected over the goal.
The Sounders host the second leg of the total-goals series on Nov. 10.