The win means Rangers could wrap up the Irn-Bru Third Division title next Saturday at home to Stirling, if nearest challengers Queen's Park slip up away to Annan.
A ticketing fiasco which caused the first Borough Briggs fixture between the teams to be postponed failed to stop fans from snapping up tickets for their final meeting of the season. Elgin oversold for the league match scheduled for November 25 and the police ordered the game to be cancelled on safety grounds.
Francisco Sandaza nearly opened the scoring on four minutes with a flashing header from Lee Wallace's cross which forced home goalkeeper Joe Malin into a brilliant one-handed save high to his right.
The Ibrox men came even closer to scoring in the 10th minute when Robbie Crawford's fierce effort from a Fraser Aird cross clipped the outside of the post.
Elgin's first chance was a Mark Nicolson free-kick which flew high over, and Craig Gunn was inches away from connecting with Daniel Moore's deflected cross in the 18th minute.
The home side almost grabbed a shock lead eight minutes before the break when they won a free-kick 25 yards out and Moore's dipping, curling strike dropped inches wide of the target.
In the second half, Malin saved from Crawford's firm strike and dealt with an Ian Black 25-yard effort to his near post just before the hour.
Sandaza just failed to turn in a diving header from Andrew Little's cross, but a Rangers breakthrough eventually arrived from the penalty spot on 72 minutes. Elgin defender Sean Crighton was penalised for a trip on Lee Wallace and McCulloch sent Malin the wrong way from the resultant penalty - the visitors' 100th goal of the season.
Rangers were largely pinned back in the closing 15 minutes, latterly with 10 men when Ian Black fouled sub Gavin Morrison and was sent off for his second booking with four minutes left.