Bryant scored 18 points in the final frame to help LA snap Houston's 12-game winning streak at home. Bryant also had six helpers and five rebounds in the contest.
Pau Gasol added 20 points and five rebounds for the Lakers, who improved to 1-1 on a three-game road trip. Josh Powell ended with 17 points and nine boards.
Yao Ming poured in 16 points and grabbed six rebounds to pace the Rockets, who dropped to 27-7 on their home floor this season. Luis Scola finished with 15 points and nine rebounds, while Aaron Brooks had 14 points. Von Wafer added 20 points off the bench in defeat.
The top sports headlines of the day
Houston committed a season-high 23 turnovers that led to 17 points for the Lakers.
Down 72-69 early in the fourth quarter, Los Angeles used a 7-1 flurry to take a 76-73 lead with 6:46 to go. With the Lakers ahead, 79-78, a little over a minute later, Bryant's three-point play extended the visitors' margin to four.
Following a pair of foul shots from Houston's Ron Artest, Bryant drilled a trey and Luke Walton went 1-of-2 from the line to give LA an 86-80 lead with 3:15 left. But the Rockets fought back with a rare four-point play from Brooks and a Wafer jumper to tie the game with under 2 1/2 minutes remaining.
On the ensuing Lakers possession, Gasol hit a pair of shots from the stripe to put the visitors up, 88-86, with over two minutes to go. From that point on it was all Bryant, as the third-leading scorer in the NBA lifted the Lakers to victory.
Bryant had a key three-point play and six free throws down the stretch, as he scored 12 of Los Angeles' final 14 points to preserve the win.
The teams were knotted at 24 after a back-and-forth battle in the first quarter.
Trailing 34-27 with under 8 1/2 minutes until half, the Rockets switched the momentum in the game by ripping off 14 consecutive points to take a 41-34 lead. Scola's layup capped off the run with over four minutes left. Carl Landry and Wafer combined to score 10 points during the surge.
Houston, which led for the remainder of the half, scored five consecutive points to finish the first half, taking a 51-40 advantage into the break.
The Rockets shot 56.1 percent from the field in the first half, while the Lakers hit 47.6 percent of their shots. Houston held Bryant to six points in the first 24 minutes.
Scola's three-point play to start the third frame extended the home teams gap to 14. But LA came roaring back with 10 straight points to cut the margin to four. Bryant tallied six points during the surge, which was topped off by a Gasol tip-in with under 8 1/2 minutes remaining.
The rest of the stanza was close, as the Rockets took a 70-67 edge into the final 12 minutes.