The City forward was denied a second five minutes before half time when Stuart Green played him through. He fired it past Keen but the linesman's flag denied him.
Alexander came out with flying colours for the second half and added to his tally within five minutes of the restart. Ryan Williams turned to find space from a throw in, and his cross was met by the unmarked Alexander to head past Keen.
The 23-year-old sealed his hat-trick in the 73rd minute after Green put him clear with a pass from his own half. Alexander was totally free to run onto it and slide it in to claim the matchball. He was substituted a minute later to a standing ovation from the 8,461 crowd.
Dudfield was denied a further three chances by dubious offside calls from the linesman, while Williams and Green also had chances to make the scoresheet in a comfortable win.
City line-up (4-4-2): Glennon; Regan (Edwards 66), Whittle, Anderson, Smith; Green, Ashbee, Keates, Williams; Alexander (Johnson 74), Jevons (Dudfield 60)
Un-used subs: Musselwhite, Bradshaw.