Gasol had 26 points and 16 rebounds, and Lamar Odom had 20 points and a season-high 20 rebounds in his return to the Lakers' starting lineup.
The two-time defending NBA champions finished their first overtime of the season on a 10-2 run, barely holding off injury-depleted Houston after losing to Sacramento and Boston in the previous four days.
Luis Scola hit a tying layup with 5.5 seconds left in regulation for the Rockets, who have lost three straight.
Kevin Martin scored 30 points while hitting four 3-pointers, and Scola added 24 points and 15 rebounds as Houston launched a season-high 38 3-point attempts. The Rockets made just 10 3-pointers on the third stop of a four-game road trip.
Odom fell two rebounds shy of his career high in another standout game in the absence of starting center Andrew Bynum, who sat out with a bone bruise in his left knee.
Los Angeles nursed a small lead through most of the fourth quarter, but after Scola's layup with 53 seconds left trimmed Los Angeles' lead to two points, Bryant missed two shots around a clutch rebound by Odom. Aaron Brooks then found Scola inexplicably unguarded beneath the Lakers' hoop for the tying score.
The Lakers got the ball to Odom on their final possession of regulation, but he simply held the ball before missing a long, off-balance jumper.
Houston went ahead 104-100 on Scola's jumper with 2:48 left in overtime, but Gasol scored four straight points to tie it. After Gasol's layup in traffic put the Lakers ahead 108-106, Scola missed a halfhearted hook shot and Bryant made a layup with 38 seconds left.
Martin has kept the Rockets largely competitive in the absence of injured Yao Ming, Brad Miller and Jared Jeffries, but Houston has lost 12 of 18 overall.
Bynum missed his first game since developing soreness in his left knee during the loss to Boston. The 7-foot shot-blocker missed Los Angeles' first 24 games while recovering from offseason surgery to repair a torn ligament in his right knee.
Coach Phil Jackson isn't certain how long Bynum will be out, suggesting he also might miss Thursday's visit from San Antonio. Bynum's fragile knees are a constant concern for the Lakers, but Odom played an inspired inside game in his absence, while Gasol took on additional minutes.
With Ron Artest and Derek Fisher hitting all the open shots they missed against the Celtics, Los Angeles jumped to a 12-point lead in the first half. Bryant embraced his role as an offensive catalyst, getting seven assists in the first quarter alone, while Gasol shouldered the extra burden of Bynum's absence with 16 points and eight rebounds.
NOTES: Rockets F Jordan Hill apparently sprained his ankle during the first half after landing on another player's foot. Hill played just three minutes. Backup swingman Courtney Lee played with an apparent case of the flu. ... Jackson used rookies Devin Ebanks and Derrick Caracter for brief stretches, attempting to give a little rest to his depleted lineup. ... Fans near courtside included actors Paul Scheer and Dennis Haysbert and Bengals LB Keith Rivers.