The achievement betters Oscar Robertson's record, set 55 years ago. Westbrook had already secured a triple-double average for the season in his previous outing.
Adams finished with a double double of 10 points/10 rebounds, but his second assist of the game proved the pivotal play.
The win raises Oklahoma City to 46 wins/34 losses for the season, with two more games remaining in the regular season, good for sixth in the Western Conference.
It also eliminated Denver from playoff contention - the eighth and final spot in the West goes to Portland Trailblazers.
The Thunder will face Houston Rockets in the first round of playoffs, providing a classic confrontation between Westbrook and MVP rival James Harden, who was traded out of Oklahoma City for the draft pick that became Steven Adams.