The Californians had to hold off their resurgent hosts in the second half.
The Lakers went to the half-time break up 53-47 and exploded at the start of the third quarter with a 10-1 run, with Anthony Davis passing the mark of 1,000 career play-off points on his way to a total of 34.
The Los Angeles offence stalled late as they lost the lead at 90-89 with less than five minutes left in the game, but they rallied to close it out 109-102.
In the Eastern Conference, the Brooklyn Nets turned to their offensive weapons to defeat the Boston Celtics 130-108 and move ahead 2-0.
Joe Harris equalled a Nets play-off record with seven three-pointers to finish with a career postseason-high 25 points, while Kevin Durant contributed 26 and James Harden 20 for the victors.
Marcus Smart top-scored with just 19 points for the Celtics, who will be sweating ahead of game three on Friday in Boston after key player Jayson Tatum left the game in the 22nd minute when he was poked in the right eye.
Back in the west, the Los Angeles Clippers led the Dallas Mavericks 73-71 at half-time but were unable to sustain their advantage, ultimately falling 127-121 to go down 2-0 in their round-one series ahead of the match-up moving to Texas.
Luka Doncic was again the main man for Dallas, putting up 39 points, seven rebounds and seven assists, while Kawhi Leonard scored 41 in a losing effort.