It was the first time in franchise history that the Giants (4-2) beat the Cowboys (3-3) on Monday night at Texas Stadium.
Barber had 114 yards rushing and another 32 receiving for the Giants, who won their third straight game and took over first place in the NFC East.
Eli Manning threw for 189 yards and tossed a pair of touchdowns; Plaxico Burress and Jeremy Shockey each caught TD passes for New York. Michael Strahan notched two of the Giants' six sacks to tie the legendary Lawrence Taylor for the franchise record with 132 1/2 in his career.
Drew Bledsoe completed 7-of-12 passes for 112 yards with an interception for the Cowboys before being benched for ineffectiveness in the third quarter.