Bryant, who sat out eight of the final 10 regular-season games to rest, got off to a slow start but found his rhythm in the second half of the Lakers' 103-88 romp over the visiting Denver Nuggets.
In San Antonio, Tony Parker scored a game-high 28 points and the red-hot Spurs silenced the Utah Jazz 106-91 - the highest offensive output by any National Basketball Association team in this year's playoffs - for their 11th consecutive win.
The West's third-seeded Lakers doubled the score on the Nuggets before the first quarter ended and Denver never came closer than four points the rest of the way.
Lakers All-Star center Andrew Bynum (pictured) tied a playoff record with 10 blocked shots to go along with the team's first triple double since 1991.
Danilo Gallinari paced Denver with 19 points.
The Lakers host Game Two on Tuesday.
For the West's top-seeded Spurs, who were upset in the opening round last year despite also being the No. 1 seed, the triumph continued an impressive April. They had closed out the regular season with a 10-0 run.
"I think everybody knows what happened last year," Parker told reporters. "I made sure I set the table in Game One by being aggressive."
Tim Duncan added 17 points and 11 rebounds while Stephen Jackson came off the bench to score 14 points for the Spurs, who at 50-16 shared the league's best regular season record with the Eastern Conference's Chicago Bulls.
Eighth-seeded Utah, which used a five-game winning streak to squeeze into the playoffs, was led by Paul Millsap's 20 points.
Game Two is Wednesday in San Antonio.
The visiting Clippers, who were blitzed by an early onslaught of Memphis three-pointers and trailed by 27 late in the third, tied an NBA playoff record of pulling off a victory after trailing by 21 points with one quarter remaining.
Nick Young scored 19 points off the bench, including a flurry of three straight three-pointers in the fourth, Chris Paul made two game-winning free throws with 23 seconds left and Los Angeles ended the game with an astonishing 28-3 run.
Memphis' Rudy Gay scored 19 but missed a shot as time expired that would have salvaged a victory which looked certain for most of the game.
“Coach took me out at the end of the third quarter and I went nuts. I just said 'coach, give us a chance," Paul told reporters after finishing with 14 points and 11 assists.
"(I thought we could win) the whole time."
Boston's Rajon Rondo may face a post-season suspension after his chest-bump with an official further soured the 83-74 home loss.
Rondo was given a technical foul for arguing a call in the final minute and quickly made matters worse by confronting referee Marc Davis and defiantly bumping him, earning a second technical and ejection.
Rondo claimed that the bump was unintentional, though the incident could see him penalised by the NBA.
"As I was walking (toward him) I thought he stopped and my momentum carried me into him," said Rondo, who had 20 points and 11 assists. “I didn't intentionally chest bump him but that's what it appears to be."