Los Blancos moved two points clear of champions Barcelona, who visit Sevilla on Sunday, as they bounced back from last week's derby drubbing.
Having returned from their long midweek trip to Kazakhstan, where they beat Kairat in the Champions League, Madrid turned their focus back to domestic matters.
Thrashed 5-2 by city rivals Atletico Madrid last weekend, Xabi Alonso's side had plenty to prove against a strong Villarreal team, who are third.
"I played very well and I want to continue like this, keeping this confidence and doing even more," Vinicius told Real Madrid TV.
"We have good feelings... when we come back (from the international break) we have big games and we need confidence," added Vinicius.
The winger did not start the season well but has found form in recent outings.
"Vini had a very good game and he was decisive, I'm very happy for him," Alonso told reporters.
Alonso brought Fede Valverde back into the team, playing him at right-back in the absence of injured duo Dani Carvajal and Trent Alexander-Arnold.
Madrid had the better of a slow-paced first half at the Santiago Bernabeu.
Teenage attacker Franco Mastantuono might have sent Los Blancos ahead but Villarreal defender Renato Veiga blocked his shot after Mbappe cut the ball back to him.
At the other end, Thibaut Courtois saved superbly from Tani Oluwaseyi, who snuck in behind the centre-backs but could not beat Madrid's Belgian goalkeeper.
Los Blancos took the lead early in the second half through Vinicius, whose shot took a fortunate deflection off Santi Comesana and flew past the helpless Arnau Tenas.
Xabi Alonso brought on Jude Bellingham for the final 25 minutes, after benching him for the second game running following the Atletico debacle.
Thomas Tuchel left the midfielder out of his England squad for upcoming World Cup qualifiers this week, and he was out to prove a point.
Tenas resistance
Madrid doubled their lead when Rafa Marin brought down Vinicius in the area and the Brazilian beat Tenas from the spot. The former Barcelona goalkeeper could have stopped the penalty but the ball slipped under him.
Alonso said that Mbappe is Madrid's main penalty taker but "it was their decision" to give Vinicius the ball.
Vinicius wanted another penalty when Tenas appeared to bring him down in the box moments later, but his appeals were waved away.
Bellingham twice came close but Tenas denied him on both occasions, with the midfielder kicking a post in frustration.
Villarreal pulled a goal back through Georges Mikautadze, who finished lethally from the edge of the box, but Madrid quickly restored their two-goal cushion.
Yellow Submarine defender Santiago Mourino was sent off for a second yellow card for a push on Vinicius as he charged down the wing, and soon Mbappe netted the third.
Brahim Diaz teed up the French superstar to roll home his ninth league goal of the campaign, making him the division's top scorer.
Mbappe was taken off grimacing in the final stages, in the only negative note for a Madrid side who were good value for their three points.
"Kylian already had a little discomfort in his ankle, we will see how it goes," said Alonso, adding that the forward would still travel to join up with the French national team.
Villarreal's Comesana complained about some of the refereeing decisions that went against his side.
"It's a shame about the first goal which hit me, and then came the penalty, which wasn't enough (of a foul) to give it," Comesana told DAZN.
"That hurt us a lot, you only have to look how he threw himself down... and the red card (was soft)... if it's already hard to win at the Bernabeu, with these things it's even harder."
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