Well, the NFL has changed the rules twice in this effect so one more tweak would make it much better (i.e. ensuring both teams get at least one possession in OT).
First rule - NFL added an OT session many decades ago. It was labeled 'sudden death' which mean the first score regardless of how it occurred would end the game. Which means tonight's game would have seen NE just run the ball a few times after getting deep in Atlanta territory and boot a winning FG (most likely, could have missed obviously) which kinda took away the climax of the win possibility.
Second rule (or first change) - Tweaked the rule to ending the game in OT on an initial drive that resulted in a touchdown. If a field goal the opposition gets a chance.
This is a stupid rule. Make it both sides get a possession or go back to the old way, which was also stupid.
Note: If the receiving team lost on a turnover, or turnover and lost thereafter, then that was their possession, obviously.