The win cemented the Catalans' 12-point lead at the top of the standings after Sevilla's 1-0 home win over Numancia, Renato's late strike settling a scrappy match and moving the Andalusians above Real Madrid into second.
Messi opened the scoring at the Nou Camp on 21 minutes when he picked up a pass from Xavi wide on the right, raced through a crowd of defenders and wrong-footed keeper Daniel Aranzubia with a low shot off the right-hand post.
Henry netted shortly after with a powerful header from a Daniel Alves cross and Eto'o drove home the rebound from Seydou Keita's header to give Barca a 3-0 lead at the break.
Aranzubia was then dismissed after he felled Carles Puyol in the penalty area (pictured) and Eto'o stroked the ball in from the spot, the league top scorer's 18th goal of the season.
"It's just one step further," he told a news conference. "There are still 19 more matches and 57 points available. We're not champions of anything yet."
Real, who host bottom club Osasuna on Sunday hoping to reclaim second spot and put Friday's resignation of club president Ramon Calderon behind them, have 35 points from 18 matches.
Depor arrived at the Nou Camp on a run of three straight defeats to Sevilla, a 3-1 reverse in the league and losses at home and away in the King's Cup, and remain in seventh.
"Football is not ludo, you have to get stuck in," he told reporters. "If we did not already have 30 points we would not sleep well tonight."
