Ulloa has now scored five goals in seven games since signing for £2million from La Liga side Almeria during the January transfer window and Poyet felt this performance was a perfect illustration of his abilities.
Brighton's third successive win puts them only two points behind fifth-placed Leicester and Poyet said: "When you sign a player like Leo you want to show to people why you signed him.
"We didn't have the kind of player he is and his second goal especially showed his quality. He has timing, jumping and power.
"During the week he was really confident and that is the key. You have to trust your own ability and he trusts his ability, especially with heading. He really believes in what he does."
Poyet is convinced Ulloa will give Brighton an extra edge in the run-in and revealed the player himself has got the aim of playing in the Premier League.
He added: "Leo wanted to come here to help us achieve what we want to achieve. To go on and play in the Premier League you need to score a lot of goals in the Championship."