Carles Alena, the 20-year-old Spaniard also regarded as a future star, came off the bench to add a late flourish, chipping in his first La Liga goal and Barca's second after a defence-splitting pass from Lionel Messi.
"Alena has earned his step up to the first team," Valverde said.
A narrow victory puts Barca back at the top of the table, two points above Sevilla, who can reclaim their place at the summit with a win away to Alaves later on Sunday night.
It also extends Barcelona's lead over Atletico Madrid, who were held earlier in the day to a 1-1 draw by Girona.
Villarreal, meanwhile, stay 17th, with the pressure mounting on coach Javier Calleja, who has overseen only one league win since September.
Alena, a dainty attacking midfielder with 13 years training in Barca's academy, is likely to enjoy many more celebrations in front of the club's fans but for Dembele, the sense was time had been running out.
Valverde's patience with the 21-year-old appeared to be wearing thin when he was left out against Real Betis three weeks ago but a late equaliser against Atletico Madrid earned a reprieve and this was another lively performance.
"He played a great game and was one of our outstanding players," Valverde said.
"He has so many assets - penetration, dribbling, shooting, speed, confidence, daring. Let's hope it continues like this." Heartening too for Valverde will have been the clean sheet, Barcelona's first in the league since the second game of the season in August.
Dembele's shot might have gone in had it not been blocked by Santiago Caseres before the Frenchman turned provider, picking out Pique with a perfectly judged cross. Pique held off Victor Ruiz, perhaps even too vigorously, and headed in.
Villarreal, however, remained in touch, literally, as Pique was lucky to escape a harsher punishment when he threw a hand into Moreno's face. When Moreno was substituted he made sure to mutter towards Pique before he departed.
Barca finally put the result beyond doubt as Messi's brilliant pass from deep freed Alena, who chipped Sergio Asenjo like he had scored dozens of goals like this rather than just his first.
Little over 100 kilometres away in Catalonia, Atletico Madrid's troubles away from home had continued as they needed Diego Costa to help them snatch a late equaliser against Girona.
Costa's excellent run and first touch panicked Girona's Jonas Ramalho into poking into his own net in the 82nd minute at Montilivi after the in-form Cristhian Stuani's penalty had fired the hosts ahead.
Avoiding defeat was enough to put a smile on Diego Simeone's face at full-time but his side have now won only once in seven league matches on the road this season.
"La Liga is barbaric," Simeone said afterwards.
"There are no easy opponents."
Girona are seventh after an excellent start to their campaign, and Stuani has led the way. His goal from the spot was his 12th of the campaign and enough to leave him top of the scoring charts, ahead of Iago Aspas and Lionel Messi.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)