Harrison Barnes scored 30 points for the Mavericks and Dirk Nowitzki had 26, including five 3-pointers.
Towns hit 15 of 19 shots from the floor as the Timberwolves shot 56.3 percent.
Rubio scored nine points in the fourth quarter, including consecutive baskets during an 8-0 run that gave the Timberwolves some breathing room after Dallas had whittled a 21-point lead to 81-77.
He hit three free throws with 2:08 to play to give Minnesota a 97-83 lead.
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MINNEAPOLIS (AP) - Karl-Anthony Towns had 34 points and 11 rebounds, Ricky Rubio added 13 points and a season-high 15 assists, and the Minnesota Timberwolves snapped a four-game losing streak with a 101-92 victory over the Dallas Mavericks on Monday night.