The game seemed set for a draw as Exeter goalkeeper Andy Marriott produced several instinctive saves to frustrate the Lions.
But Harris's ninth goal of the season ensured a deserved win for Kenny Jacket's side.
The Lions recent form has seen them clamber their way into the play-off places and their confidence was apparent as Harris, Steve Morison and Shaun Batt all saw efforts well-saved inside the opening ten minutes.
Marriot, who was enjoying something of a personal dual with Batt, denied the winger on three further occasions before the veteran stopper kept out Morison with a fine one-handed save.
Loan signing Jonathan Obika impressed as a second-half substitute with several dangerous crosses and the youngster won the free-kick from which Harris dispatched a delightful finish to secure his side's fifth successive win.
Exeter were reduced to 10-men by the late dismissal of Barry Corr and offered little threat as they slipped deeper into trouble, just one point above the drop zone.