The Quakes (3-5-5, 14 points) are 3-1-2 in six MLS matches under interim coach Alex Covelo.
Johnny Russell scored for Sporting KC (3-7-4, 13 points), who earned a point on the road for just the second time this season (0-6-2).
San Jose dominated possession in the first half, with 62 percent of the touches and attempting 10 shots, four of which reached the target. The Earthquakes finished with an 18-6 shots advantage, including 5-2 in shots on goal.
Jeremy Ebobisse pressed for the opening tally with several chances. In the 14th minute, his shot from above the arc went right of the net and three minutes later, the forward tried to connect off a drive from the left side. Ebobisse couldn't fully settle the ball at the top of the box before taking a shot that drifted high and wide.
In the 41st minute, his long-range strike appeared headed wide as Sporting KC goalkeeper Tim Melia dove to ensure it steered clear of the net.
Kansas City made the most of its limited opportunities to take a 1-0 lead in the 45th minute. Quakes goalkeeper JT Marcinowski came out to the left of the net to stop Cameron Duke and couldn't get back in time, giving Russell an open net for the easy tally.
It was the 44th goal of Russell's MLS career, moving him into sole possession of third-most regular-season goals in Sporting KC history.
San Jose responded with the equalizer early in the second half. Yueill, inside the box, headed in a feed from Jamiro Monteiro to tie it 1-1 in the 46th minute.
The home side continued to control the play, pushing to take the lead. In the 60th minute, Ebobisse's shot from the left side of the box rolled past the far post while Javier "Chofis" Lopez's attempt from above the box in the 72nd minute just missed the left side of the net.
Russell had a chance for his second of the match in the 75th minute on a sliding kick that rolled behind the net.