Gregg Berhalter's men are top of the Eastern Conference on nine points after Justin Meram's 94th-minute winner at CenturyLink Field in Washington.
Kenny Cooper gave the Sounders the lead midway through the first half with a fine finish into the bottom corner on the counter-attack.
But the game turned just before the hour-mark as former Liverpool defender Djimi Traore was sent off for denying Dominic Oduro a clear goalscoring opportunity despite the Ghanaian getting a shot away.
Federico Higuain – the brother of Napoli's Gonzalo – drilled the penalty down the middle, giving Stefan Frei no chance.
Just as it looked like the Sounders would hold on for a point, Meram delivered for Columbus.
The substitute was given a short corner with seconds remaining and his shot from just inside the area found the top corner.
Sporting Kansas City are two points behind the Crew after they also struck late to overcome the Colorado Rapids 3-2 at Dick's Sporting Goods Park.
All five goals came in the second half as Graham Zusi put Sporting ahead before a Vicente Sanchez brace had the Rapids 2-1 up.
Benny Feilhaber levelled for Kansas City on 80 minutes and Colorado were reduced to 10 men soon after when Marvell Wynne saw red.
Englishman and substitute Dom Dwyer produced the winner from a tight angle on 93 minutes.
The Houston Dynamo suffered their first loss of the season with a 2-1 defeat at the Vancouver Whitecaps.
Real Salt Lake are unbeaten in four matches this season after Alvaro Saborio's brace led them to a 3-0 win over Toronto.
Marco Di Vaio's equaliser helped the Montreal Impact draw 1-1 at Philadelphia Union and DC United and Chicago Fire played out an entertaining 2-2 draw.
Lee Nguyen's late winner saw the New England Revolution to their first win of the campaign with a 2-1 victory at the San Jose Earthquakes.
Dallas were 2-1 winners at home to the Portland Timbers as both teams finished the encounter with 10 men.
