Owens passed Chris Carter on the NFL all-time list for touchdown receptions with his 131st career touchdown catch - a 72-yard reception from quarterback Tony Romo that gave Dallas a 7-3 advantage in the first quarter.
Owens added No. 132 in the second quarter, a four-yard TD catch from Romo that put Dallas 21-20 ahead.
The wide receiver took over second place on the National Football League's all-time touchdown reception list with his 131st scoring catch and added a four-yard scoring reception from Romo with 10:02 left in the first half.
Pro Football Hall of Famer and former teammate Jerry Rice is the NFL's career leader in touchdown pass receptions with 197 touchdowns.
Terrell Owens of the Dallas Cowboys
Owens, 34, inked a three-year contract extension worth 27 million dollars in the offseason.He had five receptions for 87 yards and a score in the Cowboys' 28-10 victory over the Cleveland Browns in the first week of the season.
In his first two seasons with the Cowboys, Owens has 171 catches for 2,622 yards and 29 touchdowns.
He holds the team's single-season record with 15 scoring catches set last year.
A third-round pick of San Francisco in 1996, Owens has 887 receptions - which is ninth-best in NFL history - in 12 seasons with the 49ers, Eagles and Cowboys.
Owens has hauled in at least 13 touchdown catches in seven seasons. Only Rice has managed eight seasons with that many scoring passes.
Owens has also had eight 1,000-yard seasons, including five in a row from 2000-04.
Barber had a 17-yard touchdown reception in the third and a one-yard scoring run in the fourth to cap the scoring for Dallas, who improved to 2-0.
In a wild back-and-forth game that saw seven lead changes, Romo completed 21-of-30 for 312 yards with three touchdowns and one interception.
It was the second straight week he surpassed 300 yards.
Eagles quarterback Donovan McNabb completed 25-of-37 passes for 281 yards and a touchdown. RB Brian Westbrook
But on the Eagles' final drive, McNabb was sacked on two straight plays. He connected with DeSean Jackson on a 4th-and-17 pass but didn't get a first down and Philadelphia turned the ball over on downs with 63 seconds left.
Jackson, McNabb's favorite target in the absence of receivers Kevin Curtis and Reggie Brown, became only the second player to record two 100-yard games to start a career - the first since Philadelphia's Don Looney did it in 1940.
The Eagles took a 37-31 lead on the second play of the fourth quarter, but Dallas answered with 10 straight points.
The Cowboys pulled within 37-34 on Nick Folk's 47-yard field goal with 10:29 left, and Dallas got the ball back when Jay Ratliff recovered a Brian Westbrook fumble.
Dallas took full advantage with a 67-yard drive capped by Barber's one-yard plunge to make it 41-37.
"It's nothing to cry about," Eagles offensive tackle Tra Thomas said. "We played hard and we battled. We just made a few too many mistakes and they capitalized. We put up a lot of points. It was a big shoot-out."
By halftime, the teams had combined for 54 points, the second most for a single half in a "Monday Night Football" game.
