Kilmarnock recovered from falling two goals behind to salvage a 2-2 draw against 10-man Hamilton in the Ladbrokes Premiership.
The goal came through a spectacular strike from Miller who took aim from around 30 yards to fire a low shot into the bottom corner.
The home side were dominating possession but it was Accies who scored next with just their second effort on goal. George Oakley nodded the ball down to Davies and he thumped in a left-foot shot from just outside the box that found the bottom corner.
Killie were given a lifeline when Accies were reduced to 10 men three minutes later.
Referee Gavin Duncan took his time to make the call after Stubbs had brought down Brophy around 30 yards from goal. But after looking over to his fourth official for guidance he eventually pulled out the red card.
Accies regrouped by taking off Davies, pushing Alex Gogic into defence and sending on Darian MacKinnon. It looked like a rearguard action was imminent but they were soon creating another chance, with Hunt's shot saved.
The Killie fans were getting restless but they finally had something to cheer in the final minute of the first half. There was little power in El Makrini's shot but Owain Fon Williams made a mess of collecting it and the ball rolled into the net.
And it got even better for Angelo Alessio's men just four minutes after the re-start when they drew level. Dominic Thomas sent in a corner that was nodded back by Del Fabro for Brophy to volley into the net.
Killie pushed hard for a winner after that but Accies held firm.