The Curtis touchdown followed was easily became the turning point of the game.
The Dolphins faced a punting situation from their 36-yard line holding a 13-10 lead in the third quarter. They were playing well on defense and had not long before taken the lead with a 73-yard drive ending with Trent Green's 18-yard touchdown pass to Marty Booker.
A false start penalty moved the punt to the 31. Brandon Fields then unloaded a bomb and great coverage downfield stopped the Cowboys at their 15-yard line.
But the Dolphins were flagged for an illegal formation and had to re-punt from their own 26. That time, Patrick Crayton returned Fields' punt 49 yards all the way to the Dolphins 30-yard line.
The momentum had swung Dallas' way and it never swung back.
After Curtis' touchdown made it 17-13, Dallas, rookie Nick Folk added two field goals to make it 23-13.
Both of those field goals came after turnovers by Green, who had an unsightly five on the day.
After Green threw the third of his four interceptions, Dallas extended its lead to 17 when Terrell Owens scored on a 34-yard touchdown catch.
The Dolphins quickly marched downfield to get another touchdown on a 21-yard pass from Green to Derek Hagan, but Dallas recovered the ensuing onside kick and on the first play from scrimmage Marion Barber ran 40 yards for a touchdown that provided the final margin.
The game, fittingly enough, ended with Green getting sacked in Dallas territory.
The game started out pretty well for the Dolphins, with the defense holding Dallas to a three-and-out and the offense then marching 44 yards to set up Jay Feely's 37-yard field goal.
But the offense couldn't do much after that until the last drive of the first half when the Dolphins went from their 20 to the Dallas 27 before Feely nailed a 45-yarder off the dirt to narrow the Cowboys' lead to 10-6.
Between those two drives, Green was intercepted on a deep pass to Booker and a drive went nowhere quickly when linebacker Bradie James came in free up the middle to sack Green on second down and set up a third-and-15 from the Miami 4-yard line.
The defense, meanwhile, had their hands full with a very good Dallas offense.
The Cowboys moved the ball pretty easily after their first drive, but the Dolphins were able to limit the damage by stopping a drive at their 40-yard line and then forcing the Cowboys to settle for a short Folk field goal.
But the defense finally broke on Dallas' fourth drive of the game when the Cowboys marched 60 yards to a touchdown, a 1-yard run by Marion Barber.
The Cowboys converted two long third downs on that drive, both times on passes from Romo to Terrell Owens.