Paul Lambert named the same side that beat Bolton at the Reebok last time out and saw them go in front when Leon Barnett converted Elliott Bennet's cross on the half hour mark.
Morison then jumped above the Sunderland defence to double the Canaries' lead, heading home from close range shortly after the break.
It was Morison's first goal for the club since his £2.8m switch from Millwall in the summer.
Steve Bruce introduced new signings Connor Wickham and Dong-Won Ji in the second half, but it was Kieran Richardson who managed to pull a goal back late on as the Black Cats pushed for a draw.
Richardson collected the ball on the left hand corner of the area and drove a low shot past John Ruddy in the Norwich net to set up an interesting finish.
Despite late pressure, Lambert's side hung on to the three points to see them climb to 9th in the table.
Norwich travel to Manchester United on Saturday while Sunderland host West Brom at the Stadium-of-Light.