Saiz produced three classy finishes to set up a 4-1 win in the first round of the Carabao Cup and announce himself after a £3million move from Spanish side Huesca last month.
The midfielder opened the scoring on 13 minutes and struck twice in two minutes after the hour, becoming the first Leeds player to claim a hat-trick on his debut since Carl Shutt in 1989.
His performance saw off a Port Vale side who were level until the 60th minute but well beaten by the time fellow debutant Caleb Ekuban rounded off Leeds’ victory late on.
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The tie ended in controversy, however, after Vale manager Brown – the former Leeds midfielder – claimed Saiz had spat at defender Joe Davis towards the end of the first half.
Brown said he had asked United to substitute Saiz after the alleged incident but the Spaniard emerged for the second half to settle the contest.
Vale were reduced to 10 men in the closing stages when Gavin Gunning received a second yellow card for a foul on Gianni Alioski. Brown was also involved in a spat with Christiansen’s coaching staff.
Brown said: “I think the boys lost focus a little bit. The guy who scored three goals spits in Joe Davis’ face and it’s very hard to take.
“We asked their staff to take him off, they ignored that and he scored three goals. That’s why it was getting a bit heated down in the technical area.”
Christiansen focused on Saiz’s performance after full-time and said Leeds had seen just “a small taste” of the playmaker’s ability.
Christiansen, United’s head coach, left Saiz on the bench of the opening game of the season at Bolton Wanderers on Sunday but admitted the 26-year-old had given him a dilemma ahead of this weekend’s Championship clash with Preston North End.
“It’s obvious that the three goals of Samu were important in our win,” Christiansen said. “He’s a player who needs time.
“We know what he’s able to give and this is a small taste of what he’s able to do. He’s a player who enjoys being with the ball. You see it. If we have possession and move the ball, he has the quality and he’s intelligent with a good finish.
“I’m very pleased with his performance but it’s not a one day show. It should be a one-season show.”
Leeds will learn their second-round opponents during tonight’s draw and Christiansen, who made nine changes to his line-up against League Two Port Vale, said: “It was important to see the players who didn’t start against Bolton, and some who were not in the squad.
“It’s a good win for confidence, especially in the second half. We created several opportunities.”