And they didn't lose because Dez Bryant dropped what should have been a two-point conversion following his diving touchdown catch with 32 seconds to play.
The truth is Baltimore beat Dallas 31-29 because the Cowboys committed a litany of dumb mistakes.
Do you know how hard it is to lose an NFL game when a team gains 481 yards -- 227 rushing and 254 passing -- totals 30 first downs and keeps the ball for 40 minutes and 3 seconds?
It's virtually impossible, but give the Cowboys a handclap, because they did it.
The Cowboys finished with 13 penalties, the third time that's happened this season, for 82 yards. The Cowboys had three presnap penalties inside the Baltimore 15. Two of those drives ended in field goals instead of touchdowns.
It's just too hard to win games with that many unforced errors that result in points being given away.
And when Jason Garrett's team allows a 108-yard kickoff return for a touchdown and Tony Romo makes yet another questionable decision on a game-changing interception, the Cowboys should consider themselves fortunate they even had a chance to win it at the end.
Still, Garrett and company even screwed up that good fortune with some questionable game management. Stop me if you've heard this after previous losses.
Wasn't assistant head coach Bill Callahan supposed to help with this silliness?
Anyway, here's what happened: After an onside kick and a pass interference penalty against Baltimore, the Cowboys had a first down at the Baltimore 33 with 34 seconds left and one timeout.
Most NFL teams run three or four plays plays with that much time. Your Cowboys ran one.
One freaking play. Unbelievable.
Bryant caught a slant, a play the Cowboys successfully ran several times. This time, though, he didn't break a tackle or elude a defender. He was tackled after a 1-yard gain with 21 seconds left.
Dallas' players hustled to the line of scrimmage as the precious seconds elapsed. Finally, Romo called a timeout with six seconds left.
How is that possible?
Garrett said it took too long for guys to get lined up, and when the clock moved under 10 seconds, it made more sense to just take the field goal. Romo gave a similar story.
No one sets up a kicker -- even one as consistently good as Bailey -- to attempt a career-long 51-yard kick to win a game.
But this is exactly why the Cowboys are 15-14 under Garrett, 98-99 since the start of the new millennium and 122-123 since 1997.
These Cowboys are the epitome of mediocre, a franchise that consistently finds ways to lose. The season-opening win over the New York Giants seems much more like an aberration than the franchise-turning win it appeared to be.
Garrett, Romo and Jerry Jones each seemed a little too pleased talking about the fight and passion the Cowboys displayed against Baltimore, a team with 14 consecutive home wins.
Frankly, giving folks credit for what they're supposed to do never feels right to me.
The next thing you know, Jerry will be hanging banners for moral victories. If that's the case, then he can start with this loss because the Cowboys did everything but win.
Of course, they're 2-3 with a road game against Carolina (which had a bye Sunday) next week. Then it's home against the Giants before trips to Atlanta and Philadelphia.
At this rate, Jerry will have a couple of more banners to hang before the end of this month.
"It's not about moral victories. It's about coming in and winning," Jason Witten said. "That's the way this league operates. You've got to find a way to win these types of games -- and we will."
That remains to be seen.
Jerry keeps wanting to use the Giants and Green Bay Packers as recent examples of teams that rode the momentum of late-season hot streaks into championships. The problem, of course, is the Cowboys traditionally stink in the final month of the season.
They need to win now.
Six weeks into the season, the Cowboys are in last place in the NFC East. Ten wins is the magic number to essentially guarantee a playoff spot.
So we're already talking about Dallas needing to win eight of their last 11 games to hit that number.
Just so you know, moral victories don't count.