Ashton wins it for Norwich
Substitute Patrick Kluivert looked to have denied the hosts when his last-minute goal cancelled out a stunning 35-yard strike from Youssef Safri midway through the second half.
However, Norwich who remain bottom of the table, but now two points behind 17th-placed West Brom threw everything forward and Ashton headed in Thomas Helveg's cross to condemn Newcastle to a fourth straight defeat.