Dallas (27-14) trailed the two-time defending champions by eight midway through the third but closed the period on a 28-11 run to take control and never look back.
Kidd scored 13 points during the critical stretch, including a trio of three-pointers after previously struggling with his shot this season.
"I came in this league (as not the best shooter), so right now I'm going through a little shooting mentality. Tonight the ball was going in," Kidd told reporters.
"Were a veteran ballclub, were desperate and it showed tonight."
Los Angeles led for most of the contest before being blitzed in the third and falling behind by as much as 16 in the fourth.
"It was a lack of defense," Lakers coach Phil Jackson said.
"They had so many open shots and they started making them. They had that third quarter that got us on our heels."
Lamar Odom recorded 20 points and 10 rebounds in the losing effort for Los Angeles.
Dirk Nowitzki scored 14 points in his third game back from a knee injury that sidelined him for nine contests.
Dallas was 2-7 in his absence and has been dealing with multiple injuries this season.
(Writing by Jahmal Corner in Los Angeles; Editing by John O'Brien)