Foye had a game-high 28 points as the Clippers (32-21) earned an impressive road victory and took a two-game lead on the fourth spot in the Western Conference while dropping the Mavs to sixth.
"We want to control our own destiny. This was a potential play-off match-up and we wanted to come here and win a game," Clippers forward Caron Butler said after his team equalled their first six-game win streak since 1992.
"This is a big confidence booster for us."
The Memphis Grizzlies (29-22) leapfrogged Dallas (30-24) for fifth in the West by beating the conference-leading Oklahoma City Thunder 94-88.
For the Thunder (40-13), the loss snapped their six-game win streak and kept them from tying Chicago for the best record in the NBA.
The struggling Bulls had earlier lost to Houston 99-93 in their 11th straight game without NBA Most Valuable Player Derrick Rose. Chicago (42-13) have lost three of five while the Rockets (29-25) remain in the eighth spot in the West.
In Dallas, Los Angeles led by 14 at halftime and built their advantage to more than 20 in the third quarter Dirk Nowitzki scored 19 points but the Mavs struggled without ailing players Jason Kidd (groin) and Lamar Odom (illness).
Blake Griffin added 15 points and 16 rebounds complete with powerful dunks for Los Angeles.
The Clippers next face a cross-town showdown on Wednesday with the Lakers, who lead them by one game.