The game was decided with the first attack of the night. Phil Reid battled well to retain possession for City before beating his man and slipping the ball in to the unmarked Willy Martin.
He thought he was about to notch his tenth goal of the season until David Crawford pulled off a magnificent save, but unfortunately for the men from the central belt, the ball cannoned off Molloy and into the back of the net to give City the perfect start.
After a nightmare opening, Queens began to assert themselves. Slick passing and quick interplay saw Elgin chasing shadows for most of the opening 20 minutes.
However, the visitors could not find the killer pass in the final third and the closest they came to threatening Kieron Renton was a Frank Carroll chip that drifted harmlessly wide of the far post.
Minutes before the break, Queens Park almost caught Elgin out. A short corner saw the ball played to the back post where talisman Carroll pounced, but his powered header was impressively kept out by Renton to the delight of the City faithful.
Elgin began the second half knowing that if the scoreline remained the same they would leapfrog their opponents in the league.
Just before the hour mark the Spiders wasted the best opportunity of the match. Elgin backed off Paul Harvey whose explosive drive stung the hands of Renton, who could only parry the ball. Carroll was quickest to react and Queens Park's top scorer rounded Renton but somehow hit James McKenzie instead of the back of the net.
With just under ten minutes remaining, Queens Park almost grabbed a spectacular equaliser. Carroll's mis-hit cross bobbled and bounced as it found its way to Stuart Kettlewell, whose overhead kick flew just over the crossbar to the relief of Renton.
Right at the death, City fans had their hearts in their mouths as Queens Park came within inches of scoring. A corner from the right hand side was met by substitute Johnny Whelan who, with his first touch of the ball, directed his header towards the bottom corner until Hugh Dickson hooked it to safety.
Reid almost grabbed a second when he capitalised on some slack defending but as the City hit man raced in on goal, he was unable to lift the ball over the advancing Crawford.
As the final whistle blew Elgin celebrated back-to-back league victories, which saw them once again climb the table. Confidence is high in the ranks as City look to close in on third position.
In contrast, Queens will wonder where it's all gone wrong. An endless amount of possession but no goals cost them here as their slump down the league table continued.