Eighteen-year-old Oliver Torres also had a night to remember, marking his first competitive start for Atletico by opening the scoring in the first minute, as well as impressing with his passing range and ability to read the game.
Diego Costa also got on the scoresheet to grab his 11th goal of the season, adding an extra shine to what was a fine night all around for Diego Simeone's side.
Atleti are now just one point behind league leaders Barcelona but Betis are in real trouble, slipping into the relegation zone.
Barely 20 seconds had been played when Atletico took the lead, Oliver appearing at the back post to slot a loose ball home, completing an Atletico attack that had originated from the left hand side.
Centre back Diego Godin could have added a second after a quarter of an hour, heading wide after an inviting ball into the box from Oliver.
Diego Costa also had chances to double the lead before the break. First he powered his way past two Betis defenders before dragging his shot wide of the near post from 12 yards out, although he claimed he had been impeded by Betis defender Jordi Figueras as he shaped to shoot.
The Brazilian got into a similar position a moment later and got his shot on target but Betis goalkeeper Guillermo Sara stuck out an arm to block it.
Atleti were stronger and more precise in the second half. Stephan Andersen had to replace the injured Sara at half-time and was forced to save a half volley from Juanfran within five minutes of coming on. His next three contributions were limited to picking the ball out of the net.
First Filipe Luis and Koke played a one-two which lead to the Brazilian full-back crossing from the byline to Villa at the far post and the former Barcelona man slid home from close range.
Then the striker received the ball on the right hand side of the area and beat two defenders before lashing into the net.
Next the scorer turned provider, putting Costa clean through and this time the Brazilian was on target, rolling the ball into the bottom corner.
Unfortunately for Betis, the damage was not yet complete, and in the final minute of stoppage time, Gabi got a fifth, driving a loose ball into the far corner.