Paul McMullan set up Archie MacPhee for Elgin's opener in the fourth minute. Strikes from Jason Crooks and Jamie Duff added to Elgin's tally after the break, both set up by Paul Millar.
Craig Smith notched a late consolation for Queen's Park, who now face Stranraer in the play-offs, while impressive Elgin take on Albion Rovers.
Stranraer suffered a 1-0 defeat against Berwick Rangers at Shielfield to dampen their play-off preparations.
The visitors' David Mitchell saved Kevin McDonald's 37th-minute penalty and, as Berwick continued to dominate, David Greenhill struck the post 12 minutes after the restart.Berwick deservedly opened the scoring in the 70th minute as Stuart Noble found Danny Handling who finished coolly.
With six minutes left Berwick were reduced to 10 men when Ben Miller was sent off for a second bookable offence, but they held on comfortably.
Champions Alloa Athletic needed a late equaliser to earn a 1-1 draw against Annan Athletic at Recreation Park. The visitors started brightly and took the lead in the 31st minute when Jordan McKechnie fed Graeme Bell who finished emphatically. Annan looked due to collect a surprising three points until Stevie May equalised on the rebound in the 87th minute after Steve Masterton's shot had struck the woodwork.
Montrose ended a disappointing campaign in style with a 5-0 destruction of Clyde at Links Park. The highly rated Martin Boyle volleyed the hosts in front in the 20th minute and the striker curled home a second four minutes before the interval. After half-time, Terry Masson and Alan Campbell scored before Boyle headed home a Dougie Cameron cross in the 75th minute for his hat-trick.
Peterhead secured a top-half finish courtesy of a comfortable 2-0 win over bottom club East Stirling at Balmoor.
The hosts opened the scoring in the 12th minute when the sought-after Rory McAllister crossed for James Redman to finish clinically. Scott Ross doubled Peterhead's lead five minutes after the interval, heading home from close range after Ross Smith's header had cannoned off the crossbar.