But on 82 minutes Alex Revell pounced on a mistake from Albion keeper Boaz Myhill to take the game into extra-time.
McClean and John-Joe O’Toole were both booked on 13 minutes after the West Brom man reacted to a late challenge by grabbing the midfielder round the neck.
Town were denied on 35 minutes when Brendan Galloway, making his West Brom debut on loan from Everton, cleared superbly off the line from Harry Beautyman.
But they led less than a minute later when a cross by Brendan Moloney was thundered home from six yards by the head of Diamond.
Jonas Olsson headed a Matt Phillips corner just over but Albion equalised in the final minute of the half as McClean cut in from the right and his 20-yard shot squirmed past Adam Smith.
And they led two minutes after the break when Phillips curled a right-wing free-kick into the box and the unmarked McAuley powered home a header.