Romo tossed two interceptions in the final 3 minutes, the first one giving Green Bay a chance for the go-ahead score with the Cowboys in position to run out the clock with a 36-31 lead.
Lacy scored with 1:31 to go for Green Bay's first lead since the first quarter and after the Packers trailed 26-3 at halftime.
The Packers (7-6-1) kept their playoff hopes alive with Rodgers possibly returning next week. He was close to medical clearance, but missed his sixth straight game with a broken collarbone. He was wearing on a headset on Green Bay's sideline.
"Most guys would pack it in - 'Guys, it's not our season. Let's go home and get ready for next year,'" said Green Bay cornerback Tramon Williams, who had an interception overturned on review before a game-clinching pick that was ruled incomplete and reversed on replay. "It's not that vibe here."
The vibe in Dallas could negative for a while, with Dez Bryant walking off the field before the game ended and refusing to talk to reporters in the locker room, simply shaking his head at them after finishing with 153 yards and a touchdown.
"This is one of the hardest losses that I've experienced," Cowboys owner Jerry Jones said. "That's a shame that we've lost that ballgame."
"We still control what we feel like we can get done," Romo said. "It just doesn't feel like it right now because we let it slip away."
Behind for the first time since the first quarter, Romo threw a ball too far in front of Cole Beasley, and Williams made a diving grab that was initially called incomplete. When the video review overturned the call, Flynn ended the game with kneel-downs.
"Right now, words really have no effect," Dallas cornerback Brandon Carr said. "Complete debacle the second half. We've just got to get better, man."
Williams had an earlier interception overturned on review with Dallas clinging to a 29-24 lead. He cradled a deflected pass in his arms and had a weaving return to inside the Dallas 10, but replayed showed the nose of ball hitting the turf.
"What a feelin'!'" said Flynn, who threw for 299 yards with one interception. "As we were taking a knee, we were thinking 'Is this real? Is this happening?'"
Romo threw for 358 yards and two touchdowns, but couldn't avoid two more critical mistakes in a career at least partially defined by them.
NOTES: DeMarco Murray had 134 yards rushing and a touchdown for Dallas. ... Dan Bailey had five field goals for Dallas. Mason Crosby hit a 57-yarder for the Packers. ... Packers DE Johnny Jolly left the game with a shoulder injury. TE Brandon Bostick came out with a foot injury. ... The Cowboys ended up without their top four linebackers after Justin Durant (hamstring) and Ernie Sims (hip) were knocked out. They were already playing without Sean Lee and Bruce Carter.
Copyright 2013 by The Associated Press