With both games featuring Western Conference teams, the first-placed Lakers beat their second-placed local rivals the LA Clippers by 103-101, while the fourth-placed Jazz beat the 11th-placed New Orleans Pelicans 106-104.
The season has had to be drastically reshaped after a hiatus of more than four months.
Twenty-two of the NBA's 30 teams have gone into a bio-secure bubble at Walt Disney World, Orlando, to play out the season, with teams most likely in contention for the play-offs being invited.
The teams will play eight regular-season seeding games before the standard 16-team play-offs will get under way.
The Lakers bounced out to a strong start against the Clippers, taking a 12-point lead at quarter time, before the Clippers bit back to lead by one point heading into the last quarter.
The Lakers kept cooler heads in the dying moments, a 27-24 last quarter lifting them to the victory, with Anthony Davis showing the way with 34 points and eight rebounds. LeBron James had 16 points, 11 rebounds and seven assists, and played a crucial role defensively at the death.
Paul George took 30 points for the Clippers while Kawhi Leonard had 28.
New Orleans led 87-78 at three-quarter time but were blown away in a 27-17 last quarter.
Brandon Ingram scored 23 for the Pelicans, while Jrue Holiday had 20.
Players wore Black Lives Matter shirts before the game started and all took a knee during the anthem, linking arms as they did so.