Meeks went 6-of-11 from beyond the arc and 14-of-14 from the foul line for the Lakers, who snapped an ugly three-game skid that included a 48-point loss to the Clippers on Thursday.
"Jodie Meeks has been our most consistent performer all year," said Lakers head coach Mike D'Antoni.
Kevin Durant recorded his sixth career triple-double with 27 points, 12 assists and 10 boards for the Thunder, who have lost two in a row since a three-game winning streak.
Serge Ibaka donated 21 points and 15 rebounds for Oklahoma City, which went 12-of-35 from beyond the arc. Russell Westbrook added 20 points, eight assists and seven rebounds.
It seemed like the Thunder were going to run away with an easy victory in the early stages. Oklahoma City shot 57.1 percent from the field in the first quarter while building a 35-26 lead.
The Thunder went on to score the first nine points of the second stanza. Reggie Jackson's layup with 9:41 left made it a 44-26 contest.
But the Lakers started their comeback with a 23-7 run. Meeks made two 3- pointers during the burst that Gasol capped with a layup, cutting the gap to 51-49.
Oklahoma City took a 56-51 lead into the locker room following Ibaka's slam with 1.3 seconds remaining.
The Lakers took control with a 36-point third quarter. Trailing 70-61, Los Angeles closed out the frame on a 26-5 run. Meeks scored 20 points in the third and the home team took an 87-75 lead into the fourth.
The Thunder trailed by 18 early in the fourth before making a late charge.
Down 102-87 with 6:15 to play, Oklahoma City scored 10 straight points to make things interesting. Derek Fisher made consecutive 3-pointers to bring the visitors within 102-97.
Westbrook's explosive dunk with 57.3 seconds to go cut the gap to 110-107. Westbrook followed with a steal but was unable to connect from beyond the arc.
Kent Bazemore's layup with 15.3 ticks remaining made it a five-point contest.
"We have to do a better job of executing on the defensive end of the floor," Thunder head coach Scott Brooks said. "We had trouble staying in front of the basketball tonight. It's something that we have to continue to work on and build going forward."
Oklahoma City had won three straight against the Lakers ... The Thunder turned the ball over 17 times, leading to 21 Los Angeles points ... The Lakers went 25-of-30 from the foul line ... Wesley Johnson and Bazemore each had 11 points for the Lakers ... Jackson had 14 points and nine boards for the Thunder.