It took Ansu, who is not 17 until Oct. 31, less than two minutes to open the scoring on what was his first start for the club. Four minutes later, he teed up Frenkie de Jong following a sublime run.
Ansu only made his debut for the Spanish champions last month, becoming the youngest player to represent the club in La Liga since the 1940s. A week later, he became the club's youngest ever scorer in the top flight when he netted in the draw at Osasuna.
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He came close to scoring two more goals against Valencia and had a penalty appeal turned down before bringing Camp Nou to its feet with a sensational chip over Daniel Wass' head.
It took Lionel Messi 13 games as a teenager to score two league goals for Barca, a feat which Ansu has managed in three appearances, but Valverde warned against getting carried away.
"There's going to be a lot of hype with Ansu -- a lot," the Barca coach said in his postmatch news conference. "What we have to do is try and keep it down. Our job is to protect the player.
"But there's no denying Ansu is a player who has something special. He seems much more mature than his age. We saw things [against Valencia] that we see in training."
Valverde also urged against expecting goals and assists from Ansu in every game, stressing how difficult it is to make it at Barca.
"It's not easy to be a Barcelona player, especially for a player as young as Ansu," he said. "It's not normal to score with your first touch and to assist with your second. This performance was a bit exaggerated in that sense.
"Things will even themselves out. We want him to get to know the league and to see how complicated it is [playing for Barcelona]. The kid is still developing."
Spain coach Roberto Moreno was also among those in the Camp Nou crowd enraptured by the forward, who was born in Guinea-Bissau but moved to Spain aged six, and he said the federation were working to ensure he could be available to play for the national team.
"I'm not involved in the process but the federation are working on bringing Ansu Fati into the Spain team and then it will be the player's decision," Moreno told reporters.
"The federation always works to ensure Spain has the best players. It's very exciting for Barca to have a player who has come through La Masia [the club's academy] doing so well but he must ensure he doesn't get carried away, he must stay calm."
Defender Clement Lenglet added: "He's 16 and we have to be patient with him.
"It's true he's taking advantage of the chances he's getting and he's a good kid who deserves what's coming his way. I am really happy for him, but we must give him time because he's 16 and things can quickly change.
"I hope not, but we have to take care of him and support him when he plays."
Ansu wasn't the only player who impressed as Barca thumped Valencia to move within two points of early leaders Atletico Madrid, who were beaten by Real Sociedad on Saturday.
Luis Suarez, on his return from a calf injury, scored twice as a second half substitute and De Jong also stood out in midfield.
The Netherlands international set up the first goal and scored the second, while completing all 54 of his passes before being taken off in the second half with one eye on Tuesday's Champions League opener at Borussia Dortmund.
"We know Frenkie can get into the box and finish well when he plays a more advanced midfield role, " Valverde said.
"In that sense, he could make even more a difference taking on long shots, but we know that when he plays the deeper midfield role it's completely different."