Barca have been suffering from a dip in form in recent weeks but defeat to their rock-bottom Galician opponents never looked likely.
Alexis Sanchez put the hosts in front when he headed home a Dani Alves cross towards the end of the first half.
And Messi, on as a second-half substitute, added a glorious second with just minutes remaining by chipping goalkeeper Daniel Aranzubia to consign Depor to a seventh defeat in eight games.
Malaga had earlier failed to beat Valladolid and their 1-1 draw at the Jose Zorilla stadium and that result could see them slip out of the Champions League places by the end of the weekend.
Manuel Pellegrini rested key performers Isco and Joaquin with Wednesday's Champions League last-16 second-leg match with Porto in mind.
His team still got off to a great start when Martin Demichelis headed them into the lead after eight minutes but Manucho equalised for the hosts shortly before the interval.
A point apiece means Valladolid stay mid-table but Malaga could surrender their grip on fourth spot if Valencia win on Sunday.
Elsewhere Rayo Vallecano continued their unlikely push for a Champions League spot as they completed a comfortable 2-0 win at home to Espanyol.
An early goal inside 10 minutes by Chori Dominguez gave the Madrid side the perfect start and Piti wrapped up the points late on to move Rayo within two points of the top four.
The win all but guarantees Rayo survival with 11 games left, a welcome contrast from last term when they only avoided the drop thanks to an injury-time winner on the last day of the season.
Javier Aguirre's side have now gone three matches without a win but remain nine points clear of the drop zone.
In the late kick-off, Mallorca secured a vital 2-1 win over Sevilla to boost their survival hopes and move within a point of safety.
Alejandro Alfaro was the hero for the home side as he scored both goals to give the Balearic Island side their first back-to-back wins of the season.
Alvaro Negredo had equalised Alfaro's early opener on the hour mark but the 26-year-old winger added a second just 10 minutes later to sink his home-town club at which he started his career.
Mallorca had Javier Marquez sent off for a second yellow card in stoppage time but the strugglers held on to move above Celta Vigo into 18th place.
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