Queens took the lead in the 14th minute when good play on the right by David Weatherston saw him thread the ball in for Frank Carroll.
The number nine intelligently picked out Mark Ferry who finished well.
Elgin looked to have levelled twice in a minute. Firstly a good delivery by Steve Mackay saw Hugh Dickson head on to Martin Charlesworth.
It seemed the young striker had levelled until a last-gasp deflection saw it go out for a corner.
Moments later Stephen Low managed to find the net for Elgin but the flag was up and his goal ruled out.
City were now on top and they got the goal they deserved when Charlesworth ran through to loop a header over David Crawford in the 28th minute.
Goalscorer Ferry should have netted his second of the game for the visitors but his embarrassing miss didn't prevent Billy Stark's men from going 2-1 ahead before half-time.
Weatherston was at the heart of things once more, laying the ball on a plate for Stephen Canning to tap home from six yards.
Richard Sinclair was shown a second yellow card in the 65th minute for kicking Mark Booth in the face as Queens were reduced to ten men and then they went down to nine when Ferry stupidly got himself sent off for dissent.
Despite Elgin throwing everything bar the kitchen sink at the goal Queens held out to win.