The lead changed hands three times in a nail-biting fourth quarter before two free throws from Chauncey Billups put the Nuggets ahead 105-101 with just 13.7 seconds left.
Although Spanish forward Pau Gasol countered with two free throws for the Lakers, Billups was successful with one more attempt from the free-throw line to give Denver some breathing space with 4.3 seconds remaining.
Lakers guard Derek Fisher missed a three-point jumper shortly before the buzzer sounded and Denver were able to celebrate a thrilling comeback win after trailing by 14 points early in the second period.
Billups finished with 27 points while Linas Kleiza and Kenyon Martin weighed in with 16 apiece as the Nuggets ended a run of 11 consecutive playoff losses to the Lakers.
All-Star guard Kobe Bryant top-scored for Los Angeles with 32 points and Trevor Ariza contributed 20 as the Lakers surrendered homecourt advantage in front of a capacity crowd at Staples Center.
The best-of-seven series will now shift to Denver for Saturday's Game Three.
Having scraped past the Nuggets 105-103 in Tuesday's opener, the Lakers made a strong start with superb defense and offensive rebounding to charge 31-23 ahead after the first quarter.
They maintained that pressure early in the second period to stretch their lead to 14 points before Anthony and Lithuanian forward Kleiza, off the bench, sparked a Nuggets fightback.
With Billups and Kleiza each pouring in a three-point jumper, Denver produced an unanswered 12-0 run before going into half-time with the deficit cut to 55-54.
Although a seven-point burst from Ariza put the Lakers 71-64 up early in the third period, the Nuggets again clawed their way back to enter the fourth period just 81-80 down.
An imperious two-point jumper from Anthony gave Denver their biggest lead of the night at 91-84 with 9.06 remaining before the Lakers rallied with three-pointers from Bryant and Shannon Brown.
Two free throws from Lamar Odom gave Los Angeles a narrow 92-91 advantage which they extended to 95-93 before the Nuggets regained control in the final moments.
