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.
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."
(Reporting by Jahmal Corner in Los Angeles; Editing by Ian Ransom/Nick Mulvenney)