It just continues a theme practiced by coach Jason Garrett to take things one day, one practice and one game at a time.
But the Giants' loss to the Saints gives the Cowboys a one-game lead in first place in the NFC East with five games to play in the regular season.
The Cowboys moved into first place after their Thanksgiving Day win over Miami and waited three days to see if they would remain there alone.
It's the Cowboys first appearance in first place since the end of the 2009 season when Dallas clinched the division. That same season, the Cowboys were in first place a total of eight weeks. For three weeks, the Cowboys were tied for first and spent five more weeks in sole possession.
In the final month, the Cowboys play the New York Giants twice, Philadelphia Eagles, Arizona Cardinals and Tampa Bay Buccaneers once each and are in good shape to possibly clinch a division title and/or a playoff berth.
"It's important to stay locked in on the task at hand," Garrett said. "I think every so often as a coach you do want to provide perspective about where we've been and where we're going. But more than anything else, we continue to emphasize the importance of doing what we can do individually and collectively to be our best. We find it's best to do that on a day-by-day basis and certainly on a week-by-week basis."