It's simple. You can't predict how many balls your opponent will take at a time, but you can control the sum of the balls of two players to be 4 (A 3 B 1 A 2 B 2 A 1 B 3). The victory of the last goal means that there are four goals left. No matter how many balls you take, you can guarantee to get the last one.

So A starts with two and then eight, then B takes one, then A takes four balls, and then A wins.