IRVING, Texas (AP) Amid plenty of smiles after Tony Romo's winning touchdown pass to Jason Witten in the final seconds of the opener against the New York Giants, the Dallas Cowboys were aware of a simple reality.

They can't expect to win essentially giving away 17 points on turnovers - particularly now that All-Pro receiver Dez Bryant is expected to miss at least a month with a broken right foot.

''I don't want to temper the win,'' owner Jerry Jones said after a 27-26 come-from-behind victory Sunday night that pushed the defending NFC East champion Cowboys to 8-0 in openers against their division rival. ''Too many people worked too hard to win this game. We can play a lot better and will play a lot better.''

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The first two big mistakes gave the Giants 10 points in the final minute of the first half, starting with a 57-yard fumble return by Dominique Rodgers-Cromartie after receiver Cole Beasley lost the ball just before hitting the ground on a nice catch and run for a first down. On the next snap, Romo threw behind Witten, who tipped the ball to linebacker Uani Unga for an interception that led to a field goal.

New York went up 23-13 with 8 minutes remaining in the game when Trumaine McBride returned an interception to the Dallas 1, setting up the other touchdown for the Giants.

Perhaps even worse, two of the three turnovers put Romo and his surgically repaired back at risk. He turned awkwardly in a futile attempt to slow Rodgers-Cromartie, and was blocked into the sideline by defensive end Damontre Moore as McBride approached the end zone.

The Cowboys overcame the errors when Romo led a pair of fourth-quarter touchdown drives, the last in just 1:27 capped by the 11-yard touchdown toss to Witten, who scored the earlier touchdown as well. Romo was 11 of 12 passing for 148 yards on the last two drives and 36 of 45 with 356 yards for the game.

''When you do a lot of positive things, but you give the ball up three times in your own area and you give them 17 points, that's an issue,'' coach Jason Garrett said. ''That's a problem, and we've got to address it.''

The Cowboys recovered two more of their fumbles, including one by running back Joseph Randle on the second carry of the game with the Cowboys facing the question of who will replace 2014 NFL rushing champion DeMarco Murray.

Dallas visits Murray's new team, Philadelphia, on Sunday.

''We gave them the ball too many times on some very random things that we are not accustomed to doing,'' Romo said. ''When we give them points on some of that stuff, it's hard to overcome. And then you don't execute in little things like dropped passes and overthrown balls.''

Bryant missed both of the late scoring drives after getting injured early in the fourth quarter. Last year's NFL leader in receiving touchdowns is unlikely to return before Dallas' bye in mid-October.

Besides missing the first meeting with Murray, Bryant figures to be sidelined for a trip to New Orleans on Oct. 4 and Tom Brady's first visit to AT&T Stadium with New England on Oct. 11, the week before the bye.

The Cowboys waived tackle Jordan Mills a week after claiming him from Chicago, clearing a roster spot that Garrett said was likely to be filled by a receiver.

''The spirit that he plays with, the energy, the passion, it's really contagious. You miss all of those things,'' Garrett said. ''There aren't Dez Bryants waiting out there on the street.''

Third-year player Terrance Williams is the most accomplished receiver after Bryant, followed by Beasley and second-year man Devin Street, who was involved in Romo's second interception when safety Brandon Meriweather knocked the ball loose from him and into McBride's arms.

''We obviously have to do a better job. I have to do a better job,'' said Beasley, who set up Witten's first touchdown with another nice catch and run to the New York 1. ''We can't do that and win football games.''

NOTES: Rookie DE Randy Gregory will miss at least four weeks with a sprained right ankle. He was injured in the third quarter. ... LG Ron Leary has a groin injury, raising the prospect of rookie La'el Collins getting a shot at starting after he was inactive against the Giants. Collins was a projected first-round pick who went undrafted because his name surfaced in a police investigation of the death of a woman he knew. Collins was never implicated and signed with the Cowboys.

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