Murray had 28 points, 12 assists and eight rebounds, and made two crucial late three-pointers to snuff out a Lakers rally which threatened to make the scoreline in the seven-game series an almost-unassailable 3-0.
Jerami Grant contributed 26 points, while Nikola Jokic had 22 points and 10 rebounds.
The match was evenly poised through the first quarter before the Nuggets broke away to lead 63-53 at half-time. A strong third quarter put them up 93-75 at the last break, before the Lakers almost snatched a win with a strong finish, outscoring Denver 31-21 and including a 19-2 run.
Denver's lead was down to just four points before Murray made a three-pointer with two minutes left. His follow-up effort from distance made it a comfortable 111-99 with 53 seconds remaining.
The Nuggets already have a record this post-season of erasing two 3-1 deficits to progress, but no NBA team has come back from 3-0 down to win a series.
Denver will seek to level the series on Thursday.