Elgin had no answer to tricky Gretna winger Ryan Baldacchino and ex-Caley Thistle front man Bingham.
Bingham's first was set up by the ex-Carlise United man, who skipped past his marker to cross for Bingham to score with a scooping header in the 21st minute.
Gretna keeper Davie Mathieson pulled of a great stop 10 minutes later to deny Elgin an equaliser. Martin Harty set up Adam Nelson, but Mathieson saved his eight yard drive one handed.
Bingham should have put Gretna further ahead from the penalty spot in the 37th minute when Elgin keeper Kieron Renton pulled down Bryan Gilfillan, but he fired wide.
He made amends three minutes later when Ryan Baldacchino's corner was flicked on for him to score from close in.
Just seven minutes after the break Baldacchino created Gretna's third goal with a run and cross for Kenny Deuchar to head home - and Gretna would have had more but for City keeper Renton.
Ryan McGuffie miscued a chance wide in the 72nd minute before setting up Bingham only for Renton to save point blank.
In the dying minutes the keeper pulled off two spectacular saves, palming a fierce drive from substitute Brian Wake round the post and beating away an eight yard volley from Gretna defendeer David Irons.
City: Kieron Renton, Stuart Cumming, Allan Dempsie, Paul Kaczan, Hugh Dickson, Jamie McKenzie, Fraser Bremner, Adam Nelson (Kyle McKendrick, 85), Martin Harty (Jason McDonald, 90), Willie Martin, Iain Vigurs (Paul Napier, 78)
Subs not used: Garry Wood, Martin Pirie.