The Silver Stars (17-8) moved ahead of idle Seattle into first place in the Western Conference.
Erin Buescher came off the bench to add 13 for San Antonio before running into a hard screen set by Chasity Melvin with 3:02 left in the game. Buescher, who hit 2 of 3 3-pointers, fell to the floor but walked off after being helped by trainers. She returned to the game to play the final minute.
Becky Hammon added 14 points for the Silver Stars, who played their last home game before the break for the Olympic Games. San Antonio is 12-2 at home.
"We couldn't get over the hump," Chicago forward Candice Dupree said. "They built the lead back up after we got close, and Becky (Hammon) and Erin (Buescher) hit a lot of 3s."
Dupree scored 20 for Chicago (8-16). She hit all 10 of her free throws and grabbed 10 rebounds.
The Sky had won three of their last five heading into the game.
After San Antonio had led by as many as 14 points in the first half, Chicago got within two points when Brooke Wyckoff hit a 3-pointer 1:54 into the second half.
San Antonio quickly rebuilt its lead to seven points, but Sylvia Fowles' putback of K.B. Sharp's missed layup brought the Sky back within two points with 2:28 left in the third quarter.
The Silver Stars took control by closing out the quarter with a 9-2 run. Young scored six in the spurt, including a follow on Vickie Johnson's missed jumper that made it 54-45 heading into the fourth quarter.
"I think the game got kind of sloppy in the second quarter," Young said. "It became just a matter of getting your hands on loose balls and just finishing plays."
She was 9-for-14 from the floor with eight rebounds.
San Antonio led by as many as 15 in the fourth quarter.
"It seems like we can't stop one mistake turning into three," Sky coach Steve Key said. "And against a good team, one mistake turning into three is six points or eight points or nine points. The next thing you know it goes from a two-point game to a 10-point game."
Buescher's jump shot gave San Antonio a 33-19 lead with 4:23 remaining before halftime, but the Silver Stars went 1-of-6 the rest of the first half and Chicago scored nine straight to bring the lead down to five at the break.