League-leading Real extended their winning streak after they swept aside Eibar 4-0 at the Ipurua Municipal Stadium.
Cristiano Ronaldo bagged a brace, while James Rodriguez and Karim Benzema were also on target as Real won their 14th consecutive match in all competitions and stayed top of the Spanish summit by two points.
Ronaldo doubled the visitors' lead from close range two minutes before half-time as he scored in the 11th successive Liga game.
Benzema scored for the fifth league game in a row and Ronaldo netted a late penalty following a hand ball by Raul Albentosa to take his Liga tally for the season to 20 and add gloss to Real's dominant performance.
Messi became Liga's all-time leading scorer with a hat-trick at Camp Nou, taking his tally of Spanish top-flight goals to 253 to move past Telmo Zarra's record of 251 that had stretched back to 1955.
Sevilla, who dropped to fifth as a result of their loss, were back on level terms two minutes into the second half after Vitolo's cross was turned in by Barca full-back Jordi Alba.
Normal service was resumed two minutes later, however, Neymar steering home Xavi's free-kick with a glancing header.
Ivan Rakitic got in on the action against his former side, when he headed in Luis Suarez's cross with 25 minutes left to play.
Malaga travelled to the capital on the back of five successive league wins, but Javi Gracia's side struggled throughout the first half, with Tiago heading Atletico ahead before Antoine Griezmann doubled his team's lead in the 42nd minute.
Roque Santa Cruz pulled one back for Malaga with 26 minutes to go but Atletico sealed all three points seven minutes from time as centre-back Diego Godin nodded in the third from close range.
Meanwhile, David Moyes' coaching debut with Real Sociedad ended in a goalless draw at fellow strugglers Deportivo La Coruna.
