Diego Costa was lively from the start, and the Brazilian-born Spain striker fed Villa inside the box in the 38th minute to finish off a quick break by scoring the opener.
Villa sustained a leg injury moments later and had to be replaced by Raul Garcia.
With the home fans chanting Aragones' name throughout, Atletico came alive in the second half as Garcia found Diego Costa racing free between defenders in the 72nd and the forward beat goalkeeper Claudio Bravo with a right-footed shot for his 20th league goal of the season.
Two minutes later, Miranda headed home a corner kick out of Bravo's reach for 3-0 before Diego, who came on in the 58th for his first appearance in his return to the club, marked his return to Atletico by dribbling into the box to unleash a rising shot into goal with three minutes remaining.
"This is something nice for the players, who have made such effort and go into every single game with the same intensity and work ethic," Atletico coach Diego Simeone said. "Luis would appreciate the team's courage, since he was a courageous type with character, just like this team."
Atletico leads with 57 points, while Barcelona and Madrid share 54 points.
Jese lunged to guide Ronaldo's cross into the area beyond goalkeeper Gorka Iraizoz for the 65th-minute opener in a game that was dominated by Bilbao up to that point.
Gomez made up for earlier misses by Aritz Aduritz and Ander Herrera when he ran onto a cleared ball outside the area to rip an unstoppable shot past goalkeeper Diego Lopez in the 73rd.
The intensity boiled over moments later when Ronaldo and Gurpegi tangled, the Ballon d'Or winner's straight red card means he will miss Madrid's next game.
"It's difficult when you lose a player without reason," Madrid defender Marcelo said. "It's already difficult to score one point here but Madrid has the obligation of winning every game. So (the red card) made it tougher."
Gomez nearly scored the winner in the 85th from another volley but Lopez tipped it over as Bilbao improved to 43 points in fourth.
Earlier Sunday, Cristian Herrera's second-half goal gave Elche a 1-0 victory against Almeria to lift the club above its relegation adversary, while Ruben Castro scored two goals as last-placed Real Betis beat Espanyol 2-0 to end a four-game losing streak.
Elche improved to 24 points, two more than Almeria which is 17th. Valladolid is 18th with 20, Rayo Vallecano has 17 and Betis 14.
All games held a minute's silence in honor of Aragones, the former Spain coach who died on Saturday at age 75.
