Tony Romo threw a 49-yard touchdown pass to Miles Austin midway through the fourth quarter as the Cowboys beat the Philadelphia Eagles, 20-16, last night in the 100th meeting of the division rivals.

On the final day of the 2008 regular season, the Eagles dominated Dallas, 44-6, in a do-or-die game for both teams. Philadelphia earned a wild-card berth with that victory, won two playoff contests on the road, and advanced to the NFC Championship game, losing at Arizona.

The Cowboys (6-2) spent the whole offseason thinking about that horrendous ending. They got their revenge and took over sole possession of first place in the NFC East with their fourth straight victory. The Eagles fell to 5-3.

“Our last loss against them really motivated us to come out and play good,’’ Cowboys DeMarcus Ware said.

Romo finished 21 of 34 for 307 yards, one touchdown, and one interception.

“We executed,’’ Romo said. “I think the coaches put together a good plan. You just have to keep fighting and getting better.’’

Donovan McNabb was shaky after a strong performance in a 40-17 rout of the Giants last week. McNabb threw for 227 yards, one TD, and was intercepted twice for the first time this season.

The Cowboys began their go-ahead drive after stopping McNabb on fourth and inches at their 45. On third and 14, Romo fooled Sheldon Brown with a pump fake and hit a wide-open Austin down the left sideline to give Dallas a 20-13 lead.

“You knew he would probably get it at some point,’’ Romo said of Austin. “He’s a good player.’’

David Akers kicked a 52-yard field goal to cut it to 20-16, but the Eagles never got the ball back.

Trailing, 10-6, the Eagles seemingly went ahead when Ellis Hobbs returned the second-half kickoff 96 yards for a score. But a holding call on Moise Fokou nullified the TD.

No matter, McNabb drove Philadelphia 77 yards for the go-ahead score.

LeSean McCoy turned a short pass into a 45-yard gain. One play later, McNabb escaped the rush and found Brent Celek in the corner of the end zone to put Philadelphia ahead, 13-10.

On Dallas’s ensuing possession, Brown intercepted Romo’s off-target pass to Jason Witten and returned it 54 yards. An illegal block by Fokou negated the return to the Cowboys’ 35, and the Eagles’ drive stalled near midfield after starting at their 12.

Mike Jenkins intercepted McNabb to set up Nick Folk’s tying 33-yard field goal eight seconds into the fourth quarter.

Romo tossed a 64-yard catch-and-run pass to Patrick Crayton late in the second quarter to set up Folk’s 22-yard field goal that made it 10-6. Tracy White made a diving, TD-saving tackle to trip up Crayton.