It cut the gap to Barcelona at the top of La Liga to nine points.
Arda Turan had a hat-trick of early chances but failed to find the net as Atleti started brightly, but the game descended into a scrappy affair with both defences on top until Betis goalkeeper Adrian flapped at a corner just after the hour mark and Costa was on hand to nod home his 11th goal of the season.
Atleti's 20th successive home victory maintained their 100 per cent record at the Calderon this season, while a second straight defeat for Betis leaves them in fifth.
As when the sides met at the Calderon in the Copa del Rey a fortnight ago, Atleti flew out of the traps but this time failed to turn their early chances into goals.
Arda was first to threaten after he was played in by Radamel Falcao but his weak chip was batted behind by Adrian.
The Betis goalkeeper was then called into action twice in quick succession as he turned another drive from Arda wide and from the resulting corner tipped Gabi's fierce drive over.
Arda was then presented with another clear shooting opportunity just inside the box after a neat one-two with Domingo Cisma but he again failed to make a decent contact as his effort trickled wide.
Betis had shown nothing as an attacking force in the opening period but they nearly took a shock lead 12 minutes into the second half as Nacho's powerful drive was well held by Thibaut Courtois.
Atletico coach Diego Simeone introduced Costa for the ineffective Adrian Lopez and the Brazilian made an almost immediate impact as Falcao fired a shot from 40 yards that Adrian did well to tip wide.
Adrian flapped at the resulting corner, however, and Costa was left with the simplest of tasks to head into an empty net from two yards.
The goal forced Betis onto the front foot but the closest they came to an equaliser was a 30-yard piledriver from Ruben Perez that flashed by Courtois' right-hand post.