The Sounders appeared doomed to settle for a goalless home draw with the 2013 champions in the rainy debut match of the North American league's 19th season. But victory came after a cross in the dying seconds drew Kansas City goalkeeper Eric Kronberg off his line and Seattle star Clint Dempsey nodded a shot off the crossbar.
The rebound fell among a handful of players, but the first to put a foot on the ball was Barrett, who tapped it into the back of the net for the triumph.
The match featured replacement referees as the sanctioning group which supplies officials for MLS matches could not reach a deal with the referees' union and locked out the regular officials. Opening-match replacement referee Alan Kelly and his two assistants were among substitutes put in place to ensure the opening matches would take place.
"We have no choice," MLS commissioner Don Garber said. "The professional referee's organization had to replace those referees so we could have these games. The last thing we wanted to do was lock out those referees."
Garber said a lockout of top-flight referees became necessary after the officials would not agree to a no-strike clause in order to ensure opening matches would not be impacted. "As we grow it's a problem we're going to have," Garber said.
Elsewhere, Landon Donovan could not get the goal he needed to become Major League Soccer's all-time leading scorer as his Los Angeles Galaxy side opened the new season with a 1-0 loss to Real Salt Lake. Salt Lake goalkeeper Nick Rimando was in inspired form to frustrate the Galaxy, who were eventually undone by Joao Plata's 80th minute goal.
Federico Higuain netted twice in a 3-0 win for the Columbus Crew over DC United. Jairo Arrieta opened the scoring before Higuain got a second from the penalty spot in the 27th minute before sealing it with a stoppage-time strike.
The Houston Dynamo got their campaign under way with a convincing 4-0 victory over the New England Revolution. Will Bruin scored twice in the opening 13 minutes before Boniek Garcia made it 3-0 with 23 minutes gone. Omar Cummings added the gloss late on.
There was also a big win for the Vancouver Whitecaps as they beat the New York Red Bulls 4-1. Kenny Miller opened the scoring from the penalty spot after 34 minutes. Sebastian Fernandez then doubled the lead four minutes into the second half before Miller's second with 13 minutes left. Pedro Morales added a fourth late on before Bradley Wright-Phillips got New York on the board at the death.
FC Dallas came from behind to beat the Montreal Impact 3-2. The Canadian side led through Sanna Nyassi after ten minutes, but Fabian Castillo cancelled that out six minutes later and Blas Perez had the Texans in front with a penalty in the 24th minute. Mauro Diaz added a third at the start of the second half, and Andrew Wenger's 65th minute strike was not enough for Montreal.