Real Madrid drew 0-0 at Deportivo La Coruna to slip seven points behind leader Barcelona, which shook off the absence of key players and a recent dip in form to beat Mallorca 3-0 and secure a firm grip on the Spanish league on Saturday.
Barcelona has 68 points to Madrid's 61 with 13 game to play.
"Obviously it's a step backward," Madrid goalkeeper Iker Casillas said.
The absence of Xavi Hernandez, Carles Puyol, Daniel Alves and Victor Valdes made little difference at Son Moix Stadium as Barcelona overcame early pressure by the hosts before Messi headed home his league-leading 26th goal in the 38th minute.
Seydou Keita scooped into the area for the Argentina forward, who headed the pass forward before using his head again to guide over goalkeeper Dudu Aouate for his 42nd goal of the season.
Villa reached Sergio Busquets' well-played long-ball before Aouate and after rounding the Israel goalkeeper rolled home his 17th of the season.
Pedro's 13th goal was a long-range shot in the 66th that dipped over Aouate into the top of goal.
"There's still a lot of league left, we still have to go to Valencia, to Villarreal, to the Bernabeu, a lot to go," Barcelona coach Pep Guardiola said.
Earlier, Atletico Madrid twice rallied to secure a 2-2 draw against Sevilla and Espanyol beat Real Sociedad 4-1 to end a four-game losing streak. Also, Sporting Gijon and Zaragoza drew 0-0 in a match of relegation-threatened teams.
Sevilla scored first at Vicente Calderon Stadium when Alvaro Negredo volleyed a rising blast past goalkeeper David De Gea in the 41st minute.
Koke scored on his Atletico debut after the young forward met Diego Forlan's long ball in the 47th sending a header out of the reach of Javi Varas.
Sevilla was ahead again in the 67th through Ivan Rakitic Jose Antonio Reyes equalized nine minutes later by slipping past the defence before slotting past Varas.
Varas denied Sergio Aguero twice from close range soon after as Atletico avoided slumping to a fifth loss in six. Negredo found the crossbar late as Sevilla stayed five points behind Espanyol.
Espanyol provisionally moved two points ahead of Athletic Bilbao into fifth at the Cornella-El Prat where Luis Garcia found Alvaro Vazquez in the 41st with a quickly taken free kick before his try was helped into goal by defender Deniel Estrada.
Estrada made up for the opener by directing a free kick past goalie Carlos Kameni with his foot two minutes later, but Sergio Garcia put Espanyol ahead for good in the 54th. Jose Callejon and Javier Marquez added the insurance for Espanyol as Sociedad slipped one point behind Sevilla in sixth after its two-game winning run ended.
Sporting stayed one point ahead of Zaragoza, which was in the last relegation place.
In Sunday's other 25th-round of games, it's: Hercules vs. Getafe; Levante vs. Osasuna; Racing Santander vs. Villarreal; and Athletic Bilbao vs. Valencia.
On Monday Malaga plays Almeria.
