The Timberwolves scored 47 points in the first quarter and went on to beat the Lakers for the first time since 2007.
Martin pumped in 27 points on 11-of-23 shooting. Rubio added 12 points, 14 assists and 10 rebounds.
Kevin Love supplied 25 points with 13 rebounds, Corey Brewer added 17 points, and Nikola Pekovic helped out with 14 and 10 rebounds as the T-Wolves won at Staples Center for the first time in eight years.
Minnesota improved to 5-2 on the season.
Steve Blake drained five 3-pointers en route to 19 points and dished off eight assists for the Lakers, who trailed by as many as 29 points in the rout.