One significant perk is that the Dallas players and coaches likely enjoyed what amounts to a second bye week a lot more than if New Orleans had extended its winning streak at the Cowboys' expense.
Dallas (7-5) played three games in 11 days and managed to win all of them. That gave the Cowboys 10 days to prepare for another home game against the Philadelphia Eagles (5-6) on Sunday.
"Our guys did a really good job preparing over this last month or so knowing that we had a lot of football in a short period of time," Dallas head coach Jason Garrett said following the 13-10 win over the Saints. "They were very professional in taking care of their bodies. Getting their mind and spirit right to practice the right way and play the right way. Now we get a chance to heal up a little bit for the next three days."
Dallas has a half-game lead over Washington (6-5) heading into the Monday Night Football matchup between the Redskins and Eagles. If Philadelphia wins, the Cowboys will have a full-game lead over both NFC East rivals. If Washington is victorious, the Cowboys and Redskins will remain tied atop the division.
The Cowboys, winners of four consecutive, have to find a way to stay hot.
Lately the offense has displayed weapons on par with any group in the NFL. Ezekiel Elliott is second in the league in rushing with 1,150 yards and Dak Prescott has come alive with a new security blanket in wide receiver Amari Cooper. That's more than enough firepower to complement a defense that short-circuited the prolific Saints on Thursday night.
However, the current four-game surge isn't enough to make Cowboys fans forget about the early stages of this season when Dallas' offense was anemic and its defense gave up too many big plays.
Following the Thursday Night Football victory, Prescott acknowledged that the big win won't mean much if the team doesn't follow it up with more.
"It was a great win, but we've got a lot more to do and a lot more to get better at," Prescott said. "That's just the mindset and mentality of this team. We've got a young team that always wants to get better even in wins. We like our chances."
Dallas wide receiver Cole Beasley sprained his right foot against the Saints and is questionable versus the Eagles.