The French forward, who joined the club in 2009, netted twice in the first-half to take his Real tally to 209 goals in 446 games, moving ahead of Mexican Hugo Sanchez into sixth place on the club's all-time top scorers list.
Mexico coach Sven-Goran Eriksson was fired on Thursday, less than 24 hours after his team lost 3-1 to Honduras in a World Cup qualifier. The Swede's position has been the subject of frequent speculation after several away defeats including two World Cup reverses in Honduras and one in Jamaica.
It was Messi's 56th converted penalty in La Liga and saw him draw level with Hugo Sanchez as the league's second-top penalty taker, behind record holder Cristiano Ronaldo on 61.
Sergio Ramos has so often been Real Madrid's man of the moment but the captain saw the tables turn as his own goal helped his former club Sevilla to a 2-1 win over the La Liga leaders on Sunday, ending a record-breaking 40-game unbeaten run.
Lionel Messi overhauled Real Madrid great Alfredo Di Stefano's La Liga goals tally as Barcelona and Atletico Madrid each won on Saturday to pull three points clear of Real at the top.
Anyone who has watched the Argentine in recent years knows he can do things with a football that seem to defy the laws of physics and he does not fit into the mould of a traditional striker.
The three-horse race for the La Liga title tightened on Sunday when leaders Real Madrid drew 2-2 at city rivals Atletico and Barcelona won 4-1 at home to Almeria.