Lillard finished with 55 points and 10 assists and twice sent the game to extra periods. It was the first 55-point, 10-assist game in NBA playoff history.
Monte Morris scored 28 points, Michael Porter Jr. had 26 points and 12 rebounds, Austin Rivers had 18 points and seven assists and Aaron Gordon 14 points and 10 rebounds for Denver, which took a 3-2 lead in the first-round series.
Robert Covington had 19 points and 11 rebounds, CJ McCollum scored 18, Jusuf Nurkic finished with 13 points and 11 rebounds before fouling out and Norman Powell also had 13 points for the Trail Blazers.
Game 6 is Thursday night in Portland.
Both teams missed two shots and McCollum turned it over with 10.2 seconds left. Morris hit two free throws and the Nuggets closed it out.
Morris hit two 3-pointers and Rivers another to put Denver ahead 132-123 with 2:14 left in the first overtime. Lillard converted a three-point play but Jokic hit a soft jumper in the lane to make it 134-126 with 1:52 remaining.
Lillard hit another 3-pointer from deep, Morris missed a layup and Lillard drained a 28-footer with 22.9 seconds left to make it 134-132. Morris split two free throws and Lillard sent it to a second overtime with another 3-pointer.
The Trail Blazers took their first lead at 83-82 and headed into the fourth up 94-92. The Nuggets rallied to go ahead 103-98 on JaMychal Green's corner 3-pointer.
Portland tied it at 115 on a Covington 3, Jokic scored four straight and McCollum hit a corner 3-pointer with 13.2 seconds left to make it 119-118.
Morris hit two free throws but Lillard sent it into overtime with a 3-pointer with 3.7 seconds left.