Celta had sprung a surprise back in November with a 1-0 win at Camp Nou and they more than matched Barca for a second time in this encounter, until Mathieu - who scored in the 2-1 Clasico victory last time out - decided the game 17 minutes from time.
It could prove to be a crucial goal for Luis Enrique's side, who had earlier seen a Cristiano Ronaldo-inspired Real Madrid hammer Granada 9-1 at the Santiago Bernabeu.
Barca struggled for large parts at Balaidos, and could have been behind had Joaquin Larrivey showed more composure when presented with a glorious opportunity late in the first half.
The visitors will point to Neymar's effort early in the second period which was disallowed for offside with replays showing that to be the incorrect decision, although Mathieu's excellent header rendered that academic.
Celta's woe in front of goal was compounded late on as Fabian Orellana was dismissed in farcical circumstances - for throwing a lump of turf at Sergio Busquets.
Larrivey netted the only goal when the two sides met in the reverse fixture, and it was he who threatened first in the 11th minute with a low shot which Claudio Bravo parried away.
Barca's response was swift, with Lionel Messi - who missed both of Argentina's friendlies during the international break with a foot injury - bringing a smart stop out of Sergio Alvarez following a trademark jinking run, before Neymar sent the rebound over.
Celta continued to look dangerous, though, and Bravo had to race from his line and slide in to divert the ball away from Nolito.
Three minutes before the break, Larrivey ought to have put the hosts ahead but he lashed wildly at Orellana's pass when he had time inside the area to take a touch and pick his spot.
Barca began the second period in much more positive fashion and Neymar had a goal ruled out for offside, despite replays suggesting the Brazil forward was level with the last defender.
Messi and Nolito both fired wide for their respective sides as the game opened up, before Dani Alves snatched a golden chance wide shortly after the hour-mark.
Gerard Pique was forced into a last-ditch challenge to deny replacement Charles as the game entered the final 20 minutes, and that proved crucial as Mathieu managed to reach substitute Xavi's free-kick with a fine far-post header which went in off the crossbar.
In a bizarre conclusion, Orellana was giving his marching orders two minutes from time for aiming a lump of grass at Busquets which struck the midfielder in the neck.
Messi missed the chance to seal the win when his deft chip went over the bar, but it mattered little as Barca held on to clinch maximum points.
