The Nuggets overcame a seven-point deficit midway through the fourth quarter by forcing three critical turnovers in the final minutes and blocking Derek Fisher's three-point attempt as time expired.
"That felt just as good as hitting the game-winner," Anthony said of his game-ending block.
"Tonight it was meant for me to be out there and play defense on that last play. I made the block and saved us tonight." Denver (52-27) won its fourth straight game to move into second place in the crowded Western conference playoff race, half a game in front of Dallas and Phoenix.
NBA champions Los Angeles (55-23) played without the resting Kobe Bryant, leaving Pau Gasol to take the lead with 26 points and 13 rebounds.
Tuning up to defend their title in the playoffs, the Lakers have appeared out of sync in losing four of their last five games.
They trailed by 10 to the Nuggets at halftime and by 14 in the third before a big 20-4 run turned the game around.
The Lakers' own 87-80 lead slipped away in the fourth, though, when three-pointers and three straight free throws gave Denver a 97-94 advantage with 44 seconds to go.
J.R. Smith bolstered the Nuggets with 26 points off the bench, bouncing back from a 4-for-13 shooting performance the previous night.
Ron Artest chipped in 22 for the Lakers, who were already without center Andrew Bynum, who is out with a foot injury.
Coach Phil Jackson said that Bryant was given the option to rest and made a late decision to sit the game out after he had struggled in his previous two outings.
"I don't anticipate (him playing on Friday at Minnesota) but I'll let him make that decision," Jackson said. "He knows exactly what he needs to do to get himself ready."
In Chicago, the hosts survived some shaky free throw shooting down the stretch to beat a Cleveland team minus LeBron James.
Derrick Rose scored 24 points and Kirk Hinrich had 23 as the Bulls moved into a tie with eighth-place Toronto in the Eastern Conference. The Raptors hold the tiebreaker, but with Chris Bosh injured, Chicago's chances are looking good.
The Bulls prevailed even though Rose and Luol Deng each missed two free throws in the final 15 seconds.
Cleveland's Mo Williams scored a season-high 35 points on a night when James was rested.
In Sacramento, California, Sacramento snapped an eight-game losing streak while extending Los Angeles skid to seven.
Tyreke Evans had 28 points, six rebounds and seven assists for the Kings, who saw their 16-point halftime trimmed to eight after three quarters.
Sacramento had a 16-2 to run to start the fourth in pushing their lead to 100-78. It was the first time in nine games that the Kings topped 100 points.
Chris Kaman scored 23 points for the Clippers.
