Corey Brewer also got extended minutes with Gallinari out and he scored 16, many in transition.
The Nuggets, who were without Danilo Gallinari and Andre Iguodola, lost their third straight game after winning a season-high seven straight.
Gallinari came over in the Melo deal along with fellow starter Kosta Koufos, key reserve Wilson Chandler and emergency center Timofey Mozgov.
The Cavaliers cut the gap to 105-99 with 1:40 remaining, but Gallinari's two free throws and Faried's dunk put the game away.
"It's tough but I think Evan has all the cards to play that way, " said Danilo Gallinari, who had 11 points to go with six assists.
Danilo Gallinari scored 19 points, Kenneth Faried added 17 and Denver won their ninth straight game with a 111-103 victory over the Cleveland Cavaliers on Saturday night.
Gallinari made a driving layup and Chandler hit a 3-pointer to spark the Nuggets on a 12-0 run that put them in front 45-28 with 5:23 remaining in the second quarter.
Ignited by a driving layup by Danilo Gallinari and a 3-pointer by Chandler, the Nuggets responded with a 12-0 run that put them in front 45-28 with 5:23 remaining in the second quarter.
Gallinari, the Nuggets' leading scorer, wasn't needed as the Nuggets won their ninth straight game at home, snapped the Lakers' three-game winning streak and took the season series from their long-time nemesis 3-1.
Wilson Chandler scored 23 points in place of Gallinari, and Ty Lawson added 22 in the Nuggets' 119-108 win Monday night in which Denver outscored the Lakers 33-3 on the fast break and 78-50 in the paint.
Fans took delight when he threw up an airball in the final minute of the first half, grabbed the board himself and was going back up for the score when Danilo Gallinari knocked the ball out of his hands and off his right leg out of bounds.
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