Higginbotham netted in the third minute of time added on at New Central Park to salvage a point and cancel out Archie MacPhee's 30th-minute penalty for Elgin.
Kelty are now two points clear of Annan, who suffered a surprise 2-1 loss in Stenhousemuir’s first victory of the campaign. Thomas Orr and Adam Brown scored in the 55th and 81st minutes for the visitors before Robert McCartney's headed reply with four minutes remaining.
Stirling moved up to third, level on points with Annan, with a 1-0 home win over Forfar courtesy of Dylan Bikey.
Edinburgh beat Stranraer 1-0 at Stair Park thanks to Ouzy See's effort with 10 minutes remaining.
Cowdenbeath replaced Stenhousemuir at the foot of the table following a 2-1 loss at Albion.
Max Wright put the hosts in front, Ross Clarke equalised just before the break and Kyle Doherty then notched the winner in the 82nd minute.