Rule 17, Section 2, Article 3 grants commissioner Goodell power to reverse the game's result.
The NFL has admitted that their officials absolutely blew it during the Saints final drive of regulation in the NFC Championship game, in which Rams defensive back Nickell Robey-Coleman should have been flagged for pass interference, or a helmet-to-helmet hit.
That said, the league's admission does not change the fact that the Saints were forced to kick a field goal with plenty of time remaining, allowing the Rams to go on and win in overtime by the final of 26-23.
However, according to "Rule 17 Section 2 Article 3," as tweeted out by Saints wide receiver Michael Thomas, the NFL rulebook actually allows the league to reverse an outcome of a game affected by "unfair acts."
The rule tweeted out by Thomas reads:
"The Commissioner’s powers under this Section 2 include the imposition of monetary fines and draft-choice forfeitures, suspension of persons involved in unfair acts, and, if appropriate, the reversal of a game’s result or the rescheduling of a game, either from the beginning or from the point at which the extraordinary act occurred. In the event of rescheduling a game, the Commissioner will be guided by the procedures specified in 17-1-5–11, above. In all cases, the Commissioner will conduct a full investigation, including the opportunity for hearings, use of game video, and any other procedure the Commissioner deems appropriate."
The league has never used that rule to reverse the outcome of a game and it's almost certain they won't do so now. Instead, the Saints will just receive a public apology from the NFL and teams will likely be granted the ability to challenge such calls moving forward.