Brazilian playmaker Ronaldinho put in an impressive display, setting-up both goals as the Catalan giants continued their march towards a third successive league title.
Barcelona are on top of the table with 56 points, three ahead of second-placed Sevilla who face Osasuna later on Sunday.
Barcelona were ahead just before the break when Ronaldinho got the better of his marker before sending a delightful pass behind the backline to Argentinean prodigy Messi, who chested the ball and cracked a powerful left-footed shot into the net.
Eto'o doubled the lead six minutes after re-start when he slotted the ball past Deportivo keeper Dudu Awat as Ronaldinho released him following a series of brilliant passes.
Youngster Lopez Adrian pulled one back in the 69th minute when he capitalized on a mis-headed clearance by Giovanni van Bronckhorst to go through on goal and poke past Victor Valdes.
Elsewhere, Valencia kept their title hopes alive with a 3-2 victory over Espanyol at Mestalla.
David Villa put the hosts in front in the 12th minute but Albert Riera leveled the score three minutes later.
Spanish winger Vicente regained Valencia's lead in the 26th minute before Miguel Angulo added the third in the 59th minute.
Luis Garcia pulled one back for Espanyol three minutes past the hour mark.
Valencia are third in the league table with 50 points, six adrift of Barcelona while Espanyol lie 10th on 38 points.