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.
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.
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.
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.
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.
