Yes. It has happened on a number of occassions, most famously in the "Heidi Game" of 1968 when the Oakland Raiders scored twice in the final minute.
Since 2000, only one team. The New England Patriots scored 50 or more twice in 2007. Those games were: 52-7 v. Redskins 56-10 v. Bills
21pointsin 52 seconds by the patriots versus the jets on November 22, 2012
The Carolina Panthers scored the fewest points in the 2010 NFL season, with only 196.
Buffulo Bills
the patriots with 589
Dallas cowboys
72 by the Washington redskins
The most points scored by one team is 73, by the Chicago Bears in the 1940 NFL Championship game. The most scored by both is 113 (Washington 72, New York 41), set in 1966.
The New Orlean Saints 463 points in 2008 making them the NFL top scoring team
Saints
yes it has happened 19 times in total 12 times the team that won twice won the third game. Only 7 times did the team that had won twice lose the third time.