New York rallied from a 10-0 first-quarter deficit to help keep alive its hopes for the NFC East Division title.
Manning amassed 241 passing yards with scoring throws to Hakeem Nicks and Brandon Jacobs.
Tony Romo led Dallas with three touchdowns on a franchise-record 41 completions for 392 passing yards.
Jason Witten caught 14 passes for a career-high 156 yards.
Roy Williams made six receptions for 60 yards with two touchdowns, and Miles Austin caught a touchdown pass for the Cowboys (8-4), who dropped into a division tie with the Philadelphia Eagles.