The win sent the Catalans nine points clear of Sevilla at the top of the table and allowed them to equal their best ever start to a season with eight wins and two draws after the first 10 matches.
Sevilla will have a chance of narrowing the gap when they host struggling Real Mallorca on Sunday, while third-placed Real Madrid, who are a further point behind, travel to Malaga.
Frank Rijkaard's side still looked to be suffering the after-effects of their exertions in Tuesday's dazzling 2-1 Champions League win over AC Milan when they fell behind to a fine goal from midfielder Fran in the seventh minute.
The Depor skipper brought the ball down with his chest and then fired a powerful shot back across the area and into the top corner after former Real Madrid player Munitis had clipped in a neat cross from the right.
But Barca, who also fell behind to AC Milan in midweek, remained unflustered and with the in-form Xavi at the helm they gradually took control of the midfield.
DARTING RUNS
Live-wire striker Samuel Eto'o created a host of problems for the Depor defence with his darting runs into the area, while French midfielder Ludovic Giuly was a constant threat on the right.
A little over a quarter of an hour later they were back on level terms, Xavi slotting in from 10 metres out after Brazilian defender Juliano Belletti had cut back a fine pass from the byline following a quick free kick from Rafael Marquez.
Barca stepped up another gear after the goal, pinning the visitors back inside their own area as they put together a succession of neatly worked attacks.
The pressure soon paid off and Eto'o ran the ball into the net to score his ninth goal of the season after Giuly had picked up a miscued shot by Marquez, drawn Depor keeper Jose Molina off his line and slotted the ball into his path.
Eto'o should have grabbed another after he was put in the clear by Ronaldinho a few minutes later, but this time Molina stood up well and managed to swipe the ball away from his feet.
Barca had several good chances to stretch their lead after the break. Mexican defender Marquez went close with a diving header and Giuly shaved the post with a low drive.
But they had to settle for the 2-1 win which allowed them to equal the start the side made to the 1996/97 season when Bobby Robson was in charge.
The only negative note of the evening for the Catalans came when Belletti damaged ligaments in his left ankle in the dying minutes after the turf gave way under his feet as he controlled the ball.
Barcelona medical staff said the player would undergo tests on Sunday to determine the extent of the injury.
