Draw, equalize, tie

Probably not draw. I like equalize since I think tie needs more detail like "tie the game in the last minute" while I think equalize stands alone but either is fine.

This question depends very much on regional dialect. I would definitely use "tie" in this context (Northeastern US).

I prefer "draw" to "equalize".

I would say equalise because that's what they did in the last minute of the game. They scored an equaliser. The game ended in a draw.

In Britain we normally say draw, Americans usually say tie.