A run and cross from Rory McAllister set up Patrick Boyle for Peterhead’s opener in the eighth minute, and that would prove to be sufficient to secure the Blue Toon three points.
Only the acrobatics of Elgin keeper Kyle Gourlay prevented the hosts from extending the margin.
Clyde rise to second spot after leapfrogging Edinburgh City with a 1-0 victory over the capital side at Broadwood David Goodwillie winning and then converting a penalty in the 50th minute.
The Bully Wee had Tom Lang dismissed for a second booking but City seldom threatened a leveller and, after leading the table for most of the season, now sit third.
Annan Athletic cemented their play-off place with a hard-fought 2-1 success against eighth-placed Queen’s Park at Galabank.
Tony Wallace netted before and after the interval and although David Galt pulled one back for Queen’s Park, the Galabankies held on.
Fourth-placed Annan’s nearest challengers are Stirling Albion who climbed to fifth courtesy of a 2-1 triumph at seventh-placed Cowdenbeath.
Darren Smith headed Stirling into a 34th minute lead but was then sent off for a reckless tackle on Robbie Buchanan. David Cox then bundled home a Cowdenbeath leveller, only for Dylan Mackin to tee up Peter MacDonald for a Stirling winner in the 72nd minute.
In the basement battle at Cliftonhill, George Newell gave bottom side Albion Rovers a 15th minute lead but second-bottom Berwick Rangers rescued a 1-1 draw three minutes from time through Calum Adamson.