Sinclair fired goalwards from Paul Harvey's free-kick but the ball did not appear to cross the line as it was cleared by Elgin's Jamie McKenzie.
Queens took the lead in somewhat fortuitous circumstances after only five minutes. Mark Ferry swung in a deep free-kick from the left and Stuart Kettlewell made contact at the back post.
The midfielder appeared to be trying to help the ball back across face of goal, but his looping effort went over the head of Elgin keeper Keiron Renton and ended up in the back of the net.
It was Queens' inability to deal with cross balls that lead to the Elgin equaliser after 31 minutes.
The home defence failed to clear Adam Nelson's corner and Paul Kaczan knocked the ball home from close range.
Queens retook the lead with a cracking goal at the start of the second half.
Kettlewell rolled the ball across to Ferry on the edge of the area and he curled a fantastic first0time effort into the net from the edge of the area.
The Queens' lead was short-lived as Martin Johnson levelled within 90 seconds.
He knocked the ball home from close range following a fine cut-back from Nelson.
Elgin then went ahead for the first time in the match six minutes later as Johnson had the easy task of sidefooting the ball home from Martin Lauchlan's cross.
But Sinclair's injury-time goal sealed a valuable share of the points for Queens, despite the controversial circumstances surrounding the late equaliser.