The striker opened the floodgates with his first goal midway through the first half with a left-foot shot from Mark Nicolson’s corner.
Ten minutes from the break, Daniel Moore’s corner eluded goalkeeper David Crawford to put the home side in full command.
There was not much on the first-half evidence to suggest Montrose could mount a salvage job in the second half – and indeed Sean Crighton was not far away from adding a fourth shortly after the break with a shot which slipped just past – but they were given a lifeline in the 57th minute when Crighton handled in the area and David Gray scored with the resultant penalty to give them hope.
Elgin’s response was swift – Nicolson drilling home the fourth into the top corner from Graeme Beveridge’s pass three minutes later.
Leslie, shortly after having a “goal” disallowed, completed his hat-trick when he headed in Moore’s cross with 20 minutes left.
Substitute Adam MacLeod marked his debut by scoring a sixth to complete the rout.