The home side battled back and after 14 minutes drew level. Darren Huckerby played a left-wing corner short to Youssef Safri and he beat Boaz Myhill low to his right with a crisp right- foot drive from 20 yards.
In the 24th minute Huckerby was fouled by Damien Delaney a yard outside the Hull penalty area but Dean Marney's free-kick went wide.
Ryan France was booked for a foul on Adam Drury after 28 minutes, but Safri rather wasted the free-kick with his team-mates queuing up in the visitors' penalty area.
Norwich went ahead after 38 minutes. Once again it came from a corner. Huckerby played his right-wing flag kick to Marney and his inswinging cross was headed in at the far post by Gary Doherty.
Ashton, still suffering from the head injury suffered on Saturday, was replaced by Kevin Lisbie in first-half stoppage time.
Early in the second half Delaney was booked for fouling Marney.
Lisbie had a shot saved by Myhill's legs and Stuart Elliott forced Green to turn his curling shot for a corner.
Lisbie fired into the sidenetting after being put through by Paul McVeigh.
Calum Davenport's header was turned round the post by Myhill.
Woodhouse was booked after 72 minutes and was promptly replaced by Kevin Ellison.
Norwich withdrew Marney in favour of Jim Brennan 12 minutes from time and the home side controlled the closing stages without adding to the goal tally.