Allie Quigley had 17 points, Stefanie Dolson scored 15 and Jessica Breland added 11 for Chicago (11-16). Vandersloot, the reigning WNBA Eastern Conference Player of the Week, also had 10 assists.
Dearica Hamby scored 17 points as the Stars (6-22) saw a three-game winning streak come to an end. Sequoia Holmes had 14 points for San Antonio, and Isabelle Harrison added 10 points and nine rebounds. Kelsey Plum finished with eight points and eight assists.
Quigley had five points and Vandersloot added a 3-pointer as Chicago jumped to an early 12-2 lead on the way to a 29-18 advantage after one quarter.
Quigley hit for 10 in the opening period, and Vandersloot joined her in double figures in the second as the Sky maintained a steady lead and pulled out to a 51-37 halftime lead.
Chicago weathered a San Antonio comeback early in the third as the Stars briefly climbed to within eight points at 53-45 on a Hamby free throw. But that was close as the visitors would get, as the Sky rolled out to a 76-61 lead by quarter's end. Chicago led by as much as 24 points in the fourth quarter.
The Sky took the regular-season series with two wins in three meetings.
San Antonio is home against the Atlanta Dream on Friday, while Chicago is off until Aug. 18, when it hosts the Los Angeles Sparks.