Messi curled home a fantastic 30-yard free-kick before latching onto Philippe Coutinho's through ball to make it 2-0 during Saturday's clash.
Nabil el Zhar pulled one back but Messi scored from Ousmane Dembele's pass to complete a 45th career hat-trick.
Barca, who are seven games from an unbeaten La Liga season, are now 12 points above Atletico Madrid, the BBC reports.
They equalled Real Sociedad's record of 38 matches unbeaten across 1978-79 and 1979-80 - and are now targeting becoming the first team to go unbeaten in a 38-game season in Spain's top flight.
Atletico can narrow the gap back to nine points when they visit Real Madrid today (Sunday) (15:15 BST).
Barca are next in action on Wednesday at Roma in the Champions League quarter-final second leg, defending a 4-1 advantage from the first leg at the Nou Camp.
