Playing in his 289th league game, Messi first equaled Zarra’s record in 21st minute and then beat it in 72nd.
Messi surpassed Bilbao great Telmo Zarra’s milestone of 251 goals that had stood untouched since 1955.
Villa was made an ‘irresistible’ offer by New York City FC after which he decided to leave Atletico.
Atletico win their first league title in 18 years after rallying to 1-1 draw at Barcelona.
Win or draw against Barcelona away on final day will hand Atletico first La Liga title since 1996.
Costa missed Sunday’s 1-1 draw to Malaga but returns to try to help Atletico clinch their first domestic league title in 18 years.
Neymar, Gerard Pique and Jordi Alba were given the all-clear by medical staff for Saturday’s La Liga final clash.
The Real Madrid striker limped out of Wednesday’s 1-1 draw at Real Valladolid with a thigh strain.
Atletico coach Diego Simeone, meanwhile, is not losing any sleep over his team’s title challenge.
Ronaldo’s injury seemed to affect Real’s spirit as they were too static and predictable in possession.
Atletico lead with 88 points and Barcelona are second with 85 and Madrid have 83 points.
“The reaction of the team will stick in people’s memories,” added the the former Atletico player.
Victory at Levante would put Atletico on 91 points, while defeat for Barca against Getafe would end their title bid.
Real will be playing their 13th final in Lisbon on May 24, while Atletico have featured only once.
Alves’ teammate Neymar showed support by posting a picture of him holding a peeled banana on Instagram.