David Villa had a penalty saved shortly after halftime at a raucous Calderon stadium, packed with fans enjoying their team’s best season in nearly 20 years, and nerves were jangling when centre back Miranda rose at the back post to nod a Jose Sosa corner powerfully into the net 18 minutes from time.
Costa was felled by Elche defender Cristian Sapunaru, who earned a second yellow card and was sent off, in the 90th minute and the Brazil-born forward stroked the ball into the net for his 27th La Liga goal of the campaign, one fewer than leading marksman Cristiano Ronaldo of Real Madrid.
The victory stretched Atletico’s lead over second-placed Real, whose game at Real Valladolid has been moved to May 7, to six points. Champions Barcelona, who host fourth-placed Athletic Bilbao on Sunday, are a further point behind in third.
Under coach Diego Simeone, Atletico are mounting a genuine challenge to the dominance of vastly wealthier Real and Barca and are closing on a first La Liga title since 1996 when a team featuring the former Argentina captain won the domestic league and Cup double.
If they win their next three matches, they will be assured of the title by the time they run out at Barca’s Nou Camp stadium for the final game of the campaign.
Before the trip to the Catalan capital, they face tough games at Valencia and Levante and a home match against Malaga.
“It was a very important win and we have to carry on like this,” Miranda told Spanish television broadcaster Canal Plus.
“There are four more finals and we have to win,” added the Brazilian.
“The team knows how to suffer when we have to suffer and now we have to rest and think about the next game.”
Atletico have also blazed a trail in Europe this season, dispatching former winners AC Milan and Barca on the way to a semi-final against Chelsea, with the first leg at the Calderon on Tuesday.
Alicante-based Elche, promoted from the second division last term, are four points above the relegation places in 15th place.
(Editing by Ed Osmond)