Moran started playing as a full back with Bohemians F.C. and then Pegasus. He was spotted by Billy Behan, a Manchester United scout, who reported to United manager Dave Sexton, and Moran signed for Manchester United in February 1978. He made his senior debut on 20 April 1979 against Southampton, and was a regular player in the first team by the time Ron Atkinson had succeeded Sexton as manager in June 1981. Despite not being the tallest of defenders, Kevin was known for his strong aerial ability and was a threat in the box from corners and set pieces.