"That kid has a great future ahead of him," Villa said about Oliver. "All of us love him. He doesn't have to rush. Our fans will be able to enjoy him for years and years to come. He just needs to be patient."
The 31-year-old Villa, Spain's all-time leading scorer, ended his month-long scoring drought with a much-needed double after being overshadowed by strike partner Diego Costa since his move from Barcelona this summer.
Having gotten his pair of goals, Villa capped his best outing for Atletico by passing for Diego Costa to notch his league-leading 11th goal of the season.
Also, Mexico forward Giovani Dos Santos scored two goals and set up the opener as Villarreal rolled past Valencia 4-1 to strengthen its hold on fourth place.
Real Sociedad took out some of the frustration from its loss at Manchester United in the Champions League this week by beating up on last-place Almeria 3-0.
Sevilla edged 10-man Osasuna 2-1 for a third win in as many rounds.
Betis goalkeeper Guillermo Sara was injured while stretching to save Diego Costa's try in first-half stoppage time.
Backup Stephan Andersen replaced him but could do nothing in the 53rd to stop Villa's glancing header to angle Filipe Luis's cross down and inside the far post.
"I'm happy for the win and for feeling healthy again after a long time suffering on the pitch," said Villa, who had to turn down a call-up from Spain earlier this month with an ankle problem. "I knew I would score goals eventually. I knew that they would arrive because that's how my career has gone."
Villa hit again four minutes later when he finished off a counterattack with Betis completely off-balance. He then expertly controlled a long pass before playing Diego Costa through to roll the ball in for the fourth goal in the 65th.
Atletico's Gabi Fernandez rounded out the thrashing in injury time.
Villarreal's home victory in the regional derby lifted the promoted side to within two points of third-place Real Madrid after it lost 2-1 at Barcelona on Saturday.
"We should be very satisfied and pleased with the performance of our players," said Villarreal coach Marcelino Garcia. "We are a humble club that took it at a Valencia side fighting to be in the Champions League. Besides, we played some good football tonight."
Dos Santos crossed for striker Ikechuwku Uche to get Villarreal started in the 17th minute. Hernan Perez made it 2-0 five minutes later.
Dos Santos hit the post and had a penalty saved by goalkeeper Vicente Guita after Jeremy Mathieu tripped Uche in the area, but he made up for his missed spot kick with a deft flick with his back to the net to score from the resulting corner kick in the 49th.
After Ricardo Costa scored Valencia's goal in the 63rd, Dos Santos beat Guaita with a long strike in the 84th for his team-high sixth goal of the season.
Sociedad's Antoine Griezmann scored two headers in the 13th and 50th, while Jose Angel set up the second of those opening goals before adding a third in the 55th.
Winless Almeria has earned three of a possible 30 points.