The prolific Spain striker, sidelined for eight months after breaking his leg at the Club World Cup last December, netted twice in a 3-1 victory at the Nou Camp that eliminated third-tier Alaves 6-1 on aggregate.
The goals were his seventh and eighth in 16 appearances since his return from injury, the first a magnificent free-kick, and took his career tally for club and country to 301.
Known as "El Guaje", or "The Kid" in his native Asturian, Villa looks to be back to something near his best at a crucial time for Barca, who are top of La Liga and through to the last 16 of the Champions League.
"Every day he looks better," Vilanova, in his first season in charge after stepping up from assistant coach to replace Pep Guardiola at the end of last term, told a news conference.
"It was a complicated injury and he has worked a great deal over the summer," he added.
"He is a player who has the scorer's gift and it is important to have him in the squad."
Villa, who turns 31 on Monday, joined Barca from Valencia at the end of the 2009-10 season after stints at Sporting Gijon and Real Zaragoza, where he scored 40 goals for each club.
After netting 128 times for Valencia, he now has 40 for Barca, plus another 53 in 85 games for Spain, making him the world and European champions' record scorer, nine ahead of former Real Madrid striker Raul.
Speaking to Barca TV after Wednesday's Cup match, Villa said the "nicest" goal he had scored was an effort from the middle of the pitch for Valencia against Deportivo La Coruna, while the most important was the one against Manchester United in the 2011 Champions League final.
With Barca already leading 2-1, Villa's beautifully executed curling strike from the edge of the penalty area effectively killed off United's hopes of a comeback and helped to seal the Catalan club's second European crown in three seasons.
"When you see the statistics it makes you think you have done a good job and you feel proud," said Villa, who was declared fit only on Wednesday morning after a brief stint on the sidelines with an ankle problem.
"It's been a long time since I came through a full game and I am very pleased to have lasted the 90 minutes," he added.
With Barca leading 3-0 from the first leg against Alaves, Vilanova was able to rest regulars including Lionel Messi, Xavi, Andres Iniesta and Sergio Busquets on Wednesday and gave promising youngsters including Jonathan Dos Santos, Sergi Roberto and Gerard Deulofeu a run out.
He also handed a senior debut to 21-year-old left back Carles Planas, who Vilanova said had been rewarded for some good performances for Barca's B team in Spain's second division.
"He is a player who has quality and he is perfectly capable of playing with us," Vilanova said.
"With Adriano and (Jordi) Alba in the squad it's not going to be easy for him but this Wednesday it was the right time.
Turning to 18-year-old striker Deulofeu, Vilanova added: "Not all footballers can step up to the first team at the age of 17 or 18.
"We have to keep challenging him. He has a lot of talent but also a lot of things still to improve."