Peterhead 0-1 East Fife (agg 0-1)
East Fife will play Second Division football next season after David Muir's goal inflicted a first defeat in 12 matches on Peterhead.
Muir struck on 48 minutes in their play-off final second leg at Balmoor after Wednesday's goalless first leg.
Visiting goalkeeper Calum Antell kept out two Rory McAllister efforts as the Blue Toon looked for the equaliser.
Peterhead will find themselves in the Third Division once again next term, having finished runners-up to Rangers.
It was only the Fifers' third win in their last 21 games, but it was enough to edge out Peterhead, who had won 10 successive matches prior to the midweek stalemate.
Both sides showed their intentions early on, McAllister firing off target for the hosts from distance before Paul Willis volleyed over for the Fifers.
Collin Samuel and McAllister, again, tried their luck before Peterhead striker Andrew Rodgers forced Calum Antell into a block.
Opposite number Smith did well to tip Paul McManus's drilled effort around a post, while Antell did likewise to keep out a free-kick from the lively McAllister at the other end.
The tie was finally blown wide open only three minutes after the break as Craig Johnstone's inswinging corner was converted right-footed from close range by Muir, whose third goal of the season followed his effort in East Fife's play-off semi-final victory over Berwick Rangers.
Antell again denied McAllister with a fine save before Peterhead's chances dried up, with the hosts racking up more bookings than goalscoring opportunities as the clash entered the closing stages.
McAllister, Peterhead's most likely source of an equaliser, twice fired off target in the final six minutes, with Willis denied a second for the Fifers by Smith.
Ross Smith then had his stoppage-time header blocked by Scott Durie as Peterhead suffered their first defeat since the start of March and East Fife remained in the Second Division.
Peterhead: Graeme Smith, Sharp, Scott Ross, Ross Smith, Noble, Redman, Cowie, Gilfillan (Bavidge 81), Cox, McAllister, Rodgers. Subs Not Used: Jarvie, McCann, McGlinchey, Fitzgerald.
Booked: McAllister, Ross Smith, Scott Ross, Rodgers.
East Fife: Antell, Durie, Campbell, White, Johnstone, Willis, Muir, Darren Smith, McBride, Samuel, Paul McManus (Robert Barr 74). Subs Not Used: Michael Brown, Gormley, Sloan, Keenan.
Booked: Darren Smith, White, Muir.
Goals: Muir 48.
Ref: Kevin Clancy