Morrison scored with a simple tap-in to convert a cross from Tom Soares, who did well to reach the byline.
Just before Morrison's goal Hull hit the woodwork when Nicky Barmby's placed shot rebounded back into play.
With 90 minutes on the clock, Andy Johnson broke clear and tucked the ball past Boaz Myhill to give Palace a third successive league win.
Hull boss Peter Taylor:
"I'm delighted with the way we have played against one of the promotion
"We matched them for long periods and passed the ball well. Each game we play we are getting more confident.
"You have to be patient when you come here and we were. We had chances and restricted Palace in the second half apart from a sloppy goal at the end."
Crystal Palace: Kiraly, Boyce, Ward, Fitz Hall, Borrowdale, Soares (Riihilahti 65), Hughes, Watson, Morrison (Butterfield 75), Johnson, Macken (Andrews 89).
Subs Not Used: Popovic, Speroni.
Booked: Johnson, Macken, Watson.
Goals: Morrison 27, Johnson 89.
Hull: Myhill, Coles, Delaney, Cort, Edge, France (Price 62), Welsh, Woodhouse (Ellison 76), Elliott, Barmby (Green 62), Brown.
Subs Not Used: Burgess, Duke.
Ref: K Wright (Cambridgeshire).