LOS ANGELES (AP) - After losing the first three games on their West Coast trip, getting a win in the finale should let the Memphis Grizzlies rest easier on the flight home.

Rudy Gay scored 18 points and Mayo had 12 of his 16 in the fourth quarter, helping Memphis avoid a winless trip by beating the Los Angeles Lakers 102-96 on Sunday night.

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The Grizzlies righted the ship after dropping six of eight games coming in, slowly sliding down the West's playoff standings in the process.

``It's much easier to sleep at night,' Grizzlies point guard Mike Conley said of the win. ``And I think guys haven't been sleeping well the last week. It's good to get a win.'

Conley had 13 points and eight assists and Tony Allen scored 12 for the Grizzlies, who squandered a 14-point third-quarter lead before pulling away in the fourth.

``We got off to a really good start,' Memphis coach Lionel Hollins said. ``Our starters came out and played with a lot of heart and passion. We played with a renewed energy and renewed spirit that we haven't played with in a while.'

Andrew Bynum scored 30 points on 11-of-16 shooting to lead the Lakers. Kobe Bryant finished with 18 points after a slow start and Ramon Sessions also had 18 in his second start with Los Angeles. Pau Gasol had 16 points on just 4-of-15 shooting while adding 14 rebounds.

``We can't ignore what's going to make us a great team, and what's going to make us a great team is playing defensively and solid at that end of the floor,' Gasol said. ``Offensively, whether we play better or not, we just have to be more consistent on the defensive end of the floor.'

Mayo accounted for all the points during a 7-0 run in the fourth, which saw the Grizzlies' lead swell to 89-76 and prevent the Lakers from winning a second time while overcoming a double-digit deficit against them this month.

Memphis bounced back from a 101-85 loss to the Clippers in the same building Saturday.

``We were pretty fed up with the way we've been playing the last 10 games,' Mayo said. ``We haven't been playing our best basketball and we feel like we're a much better team than we have been putting out there. It's a step out of the mud. It's time to get rolling.'

The Grizzlies took their largest lead at 65-51 early in the third. The Lakers then came alive on the offensive end, scoring the next 15 points and grabbing a 66-65 lead on Sessions' 3-pointer.

But the lead was short-lived as Memphis answered with an 8-0 run. Matt Barnes was whistled for a technical when he whipped the ball at Marc Gasol. Mayo requested to take the free throw, hoping to get into a rhythm.

The ploy worked. He made the freebie, Hamed Haddadi made a short hook to make it 73-66, and Mayo caught fire minutes later.

``After that, once I saw one go in the basket, it was a good feeling to let loose a little bit,' Mayo said.

The Lakers had crept back in when Bynum made one of two from the line to cut it to 78-74. Randolph hustled for an offensive rebound and putback and Mayo drove the length of the floor for a layup.

A jumper by Bryant momentarily provided a stopgap, until Mayo converted a pair of layups around a 3-pointer from the wing to give the Grizzlies an 89-76 lead.

``Tonight was one of those games were the energy wasn't really there,' Sessions said. ``We turned it on in the second half to cut the lead down, but they went on another run and it was a little too late at the end.'

As the Lakers attempted to make a final push, Bryant sat on the bench for nearly four minutes, a rare occurrence for one of the NBA's most dangerous closers. Bryant didn't appear to agree with the move in the locker room after the game but said he supports Mike Brown's decision.

``If you guys are looking for a story, I'm not going to give it to you,' Bryant said. ``I can't sit here and criticize his decisions. As the leader of this ball club, that's something I can't afford to do.

``I've had his back the whole season. I can't start doing something crazy now. That would make no sense.'

Bryant wasn't involved in the offense early as the Lakers missed their first seven shots. He attempted just one shot in the opening nine minutes, missing a jumper, before hitting a 3-pointer from the wing for his first points.

Bryant later had a layup for his only other basket of the half, shooting 2 of 7. Pau Gasol also struggled, missing his first four shots in going 2 of 10 at the break.

NOTES: The Lakers rallied from a 17-point second-half deficit in beating the Grizzlies 116-111 in double overtime March 13. ... The Grizzlies avoide losing four straight on the road for the first time since a six-game slide Nov. 15-Dec. 6, 2010. ... Zach Randolph was playing his sixth game since returning from the injury. He had 10 points and 12 rebounds off the bench against the Lakers after starting the three previous games. . Marreese Speights and Haddadi also scored 10 each as seven Grizzlies were in double figures.