When I finally won the first game it went into overtime. The score was 1:1 and I got lucky and scored first.

Your first priority is to get Tidus leveled up so he can use a special technique. Just keep passing the ball between them, it's also a decent way to keep the other team from scoring. If you keep control of the ball and stick with safe passing your characters will gain xp and might level up for a chance at winning in the second half. For Tidus you'll either be using the Jecht Shot or the Sphere Shot depending on the outcome of the minigame on the boat. Don't be concerned about the cost of using special skills, keep shooting. Halfway through the second half Tidus leaves and Wakka comes in so you have a fresh player. Between the two you should be able to score a point or two. And if you managed to keep control of the ball the entire first half the opposing team shouldn't have scored.