Houston had up to 48 hours from the conclusion of the game in question to do so.
The Rockets will now have five days to compile sufficient evidence to prove that the outcome of the game was affected by James Harden's disallowed dunk, according to Tim Reynolds of The Associated Press.
NBA commissioner Adam Silver will then have another five days to decide where or not he'll uphold Houston's protest, Reynolds adds.
The Rockets' case will reportedly center around the referees' refusal to recognize Harden's made basket, as they'll argue it constituted a "misapplication of rules."
Houston was up 102-89 with 7:50 remaining in the contest at the time of the incident. The game would be replayed from that point if the Rockets' protest is successful.
The last NBA protest to be upheld stemmed from a game between the Miami Heat and Atlanta Hawks on Dec. 19, 2007. The Hawks had defeated the Heat 117-111 in overtime, but the official scorer incorrectly ruled that Shaquille O'Neal had fouled out.
Miami successfully appealed and the teams replayed the final 51.9 seconds of the game just prior to their next meeting in March 2008. The final result didn't change, as the Hawks held on for a 114-111 victory.