The champion Lakers were able to lean on their defense, holding Memphis to 39 second-half points in their triumph.
"Defensively, we did a decent job of stopping the ball and shut their bigs (big players) down," Lakers center Andrew Bynum told reporters after collecting 11 points.
"I don't know how many turnovers they had, but we got a lot of stops and that's what did it for us."
Out of sync offensively for much of the night, the Lakers missed 14 free throws and shot just 43 percent from the field while All-Star Bryant committed six turnovers.
Los Angeles pulled it together in the fourth where they led 78-76 midway before embarking on an 11-0 run that sealed the win.
Sam Young had a team-high 22 points for the Grizzlies (27-26), who fell to their second straight loss after enjoying a five-game winning streak.
Rudy Gay added 18 points and eight rebounds for the home team which trailed for most of the night.
The Lakers will now prepare for their rematch with rival Boston on Thursday after the Celtics emphatically beat Los Angeles 109-96 on Jan 30.
The Celtics and Lakers have met in two of the last three NBA Finals, with each team capturing one series each.
"We want to see how much we improved since the last time we faced them," Bryant said. "Obviously, it's a short turnaround from the last time but still it's a good test."
(Writing by Jahmal Corner in Los Angeles; Editing by Frank Pingue and Patrick Johnston)