Six-times All Star point guard Paul scored a game-high 23 points on seven-of-11 shooting, along with seven assists, as the Clippers drew first blood in their best-of-seven Western Conference first-round series.
Eric Bledsoe weighed in with 15 points off the bench, veteran shooting guard Chauncey Billups contributed 14 and both Caron Butler and Jamal Crawford delivered 13.
Back-up guard Jerryd Bayless led the way for the Grizzlies with 19 points while Spanish center Marc Gasol added 16, but the visitors paid a hefty price for being out-rebounded 47-23.
"We got beat at our own game," Gasol told reporters after the Grizzlies, known for their physical style and gritty defense, were outshot from the field by 55.4 percent to 46.5 in front of a packed house at the Staples Center.
"We gotta give them credit. Once we got a stop, they kept running in and getting offensive rebounds and second-chance points. They were doing a good job of trying to get us away from what we're trying to do.
"We've got to regroup. We have to play better. We cannot have 23 rebounds and they can't have 40-something rebounds. That's too much of a difference because that's our game."
The two teams fought out a seven-game thriller in the opening round of the playoffs last season but on Saturday the fourth-seeded Clippers were always in control.
They raced into a 13-point lead early in the second quarter and though the fifth-seeded Grizzlies cut the deficit to just one early in the fourth, the home team again pulled away.
Paul made a pair of free throws, poured in a three-pointer after teasing Bayless with his dribbling skills from beyond the arc, then got the steal which led to a Bledsoe finger roll layup that put the Clippers ahead 104-87.
With just over two minutes left on the clock, Game One was effectively over.
"It was a really good performance from us, a total team effort," Clippers coach Vinny Del Negro said. "I was pleased with the way we rebounded the basketball tonight.
"Our overall effort on the glass was very productive, our guards did a good job getting in there and getting rebounds.
"Both teams got into some foul trouble with some key players, but we were able to battle through. As we went down the stretch, we made some shots."
Twice All Star Blake Griffin was held to 10 points and five rebounds before fouling out with 3:32 left after spending much of the game trying to outmuscle Grizzlies power forward Zach Randolph.
"I'm ready for however many games it's going to take," said fit-again Griffin, who had suffered back spasms during the regular-season finale on Wednesday. "If that's the way he (Randolph) wants to play, let's do it.
"That's his whole M.O., to frustrate guys and do his thing under the basket and play a physical game. But I like playing physical, too. So, we'll see."
Game Two is back at the Staples Center in downtown Los Angeles on Monday.
- Sports & Recreation
- Eric Bledsoe
- Jerryd Bayless