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 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."
After the Jazz held the regular season's second-highest scoring team to just two points in the game's first two minutes, the Spurs went on an 8-0 run late in the first quarter to grab control and broke open the contest with 31 points in the third.
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.