Atletico Madrid's eighth straight win in the league kept it in control of its destiny and needing three wins in the final four rounds to claim its first league title since 1996.
Defender Miranda scored the opening goal at Vicente Calderon Stadium in the 72nd minute when he floated his header just inside the upright before Diego Costa added a penalty he had earned in stoppage time for his 27th league goal of the season.
Atletico Madrid needed goalkeeper Courtois Thibaut to make successive saves around the half-hour mark, and didn't lose its composure after David Villa had a penalty saved in the 51st.
Atletico Madrid provisionally extended its lead over Real Madrid to six points, with Barcelona another point behind.
Madrid won't play Valladolid until May 7 as it rests after winning the Copa del Rey title and prepares to host Bayern Munich on Wednesday in the other Champions League semifinal.
Barcelona hosts Athletic Bilbao on Sunday needing to rebound from losing in the Copa del Rey final and keep alive its dwindling hopes of defending its league title.
Regardless of the two powerhouses' results, Atletico can break their combined nine-year hold on the league crown by winning three of its four remaining games at Valencia and Levante, then home against Malaga, before the season finale at Barcelona.
''All the games here on in are going to be tough,'' said Atletico Madrid coach Diego Simeone. ''We have made it through one `final' and have four to go. I don't even want to think that winning three will be enough. All our effort and work make us focus on the four games left, and three are away from home.
''Now we need to recover the best we can for Chelsea, a game that is very important for us, our fans and the history of the club.''
Diego Costa showed no signs of the deep cut in his left shin he received last week when he slammed into the goal post while scoring at Getafe, with the Brazilian striker causing Elche's defense trouble from the start.
He earned a penalty when fouled from behind by Ionut Sapunaru, who was sent off with his second yellow card, giving Diego Costa the chance to pull within one goal of Cristiano Ronaldo's league-leading tally of 28 goals for Madrid this campaign.
Courtois did his part by making saves to deny Javi Marquez and Sapunaru, again proving his major contribution to Atletico Madrid's championship bid.
Simeone sent on midfielders Raul Garcia and Jose Sosa early in the second half, and both set up scoring opportunities.
Raul was fouled to produce a penalty, only for Villa to have his spot kick smothered by goalie Manuel Herrera before he was replaced by Sosa.
Sosa picked out Miranda at the far post for him to lift his corner kick into the side of the net and set Atletico Madrid on its way.
''It was a set piece we had worked on,'' said Miranda, the latest role player to step up at big moments and score key goals for Atletico Madrid. ''We know how to dig down when we have to. We have four finals left and we have to win them.''