A recently signed fullback lost a fumble. The quarterback threw a bad interception. An eight-point lead became a nine-point deficit. Murray lost 9 yards on a third-and-goal at the 1.
"Today we felt like we were playing for everything," Romo said. "Next week will be the same thing."
The Cowboys, who beat Philadelphia 17-3 on Oct. 20, set themselves up to quash two years of 8-8, collapse-around-Christmas misery.
"I know in some ways we've gotten hit with just the fact of losing the last couple of years in the final game," Romo said. "I think we're the only team that keeps getting themselves in position to win the NFC East every year - that's a credit. It's also a negative in the fact that we didn't do it the last couple of years."
On Sunday, the Cowboys fell flat in the third quarter instead of the fourth, leaving just enough time for a comeback.
"Coming back and playing well and working hard can help your character. Now, I don't recommend the way we came back today as a way to get there," Dallas owner Jerry Jones said with a smile. "I would've liked for it to be a little easier and confident."
Pierre Garcon (11 catches, 144 yards) provided the home team highlight by breaking Art Monk's single-season franchise reception record, while veteran linebacker London Fletcher played in what is expected to be his final home game before retiring. Embattled coach Mike Shanahan clinched his worst record in his 20 seasons as a head coach.
"Everybody on the team is fed up at this point," Washington linebacker Perry Riley said. "We should be winning. Need to be winning. We're not winning. And that's frustrating."
Romo completed 17 of 27 passes for 226 yards with two touchdowns and played much of the game with back pain. He was limping noticeably after a couple of plays in the fourth quarter.
"I took a hit that kind of triggered it a little bit. ... I felt it after that play, the rest of the game," Romo said. "You just play through it, just like anything in football."
But Romo converted a fourth-and-6 at the Washington 40-yard line to set up a field goal that cut the lead to six with 6:09 to play. The Cowboys started the go-ahead drive at their 13 with 3:39 remaining. A 51-yard pass to Terrance Williams set up the winning score, with the Cowboys surviving the 9-yard loss by Murray when knocking on the door at the 1.
"A couple of self-inflicted wounds in the second half hurt us," Dallas coach Jason Garrett said. "But you keep playing. Our guys scratched, clawed, and fought."
Notes: Michael Spurlock, signed Wednesday because of an injury to Dwayne Harris, set up a TD with a 62-yard punt return in the first quarter. ... Murray ran for 96 yards, becoming the first Cowboys back to rush for 1,000 yards since Julius Jones in 2006. ... The Cowboys are 5-0 in the NFC East; the Redskins are 0-5. ... Injuries: Cowboys RB Phillip Tanner (head) and Redskins LBs Brian Orakpo (right groin) and Nick Barnett (sprained left knee).
Copyright 2013 by The Associated Press