Rubio scored 21 points to go with 13 rebounds and 12 assists. J.J. Barea came off the bench to score 17 points.
Minnesota had lost eight of its last nine games coming into the contest. The Spurs, who lost their second game in six starts, hit the floor without Tim Duncan and Kawhi Leonard, who stayed in Texas with injured point guard Tony Parker to rest their sore knees.
Cory Joseph led San Antonio with 15 points and Stephen Jackson added 14. The Spurs shot 35 percent from the field and scored 10 points in the second quarter.