It was the home team that enjoyed the majority of the chances in Vigo, but Mathieu's second league goal of the season ensured that Barcelona regained their four-point lead at the top of La Liga.
Celta, meanwhile, who finished with 10 men following a late red for Fabian Orellana, remain in 11th position following a third league defeat in four matches.
Here, Sports Mole dissects the 90 minutes of action.
On target: 1
On target: 3
Was the result fair?
Celta put so much into the game that they will feel extremely disappointed not to have taken something from the match, but Barcelona will argue that their dominance in the second period deserved to bring about all three points. Both teams struggled to create chances in a cagey first 45 minutes, but it was Celta that looked the most likely. Joaquin Larrivey had a golden opportunity to send Celta ahead late in the first period, but he fired over the crossbar during a period where Barcelona were struggling to keep hold of the ball. The visitors did have the ball in the back of the net minutes into the second period, but Neymar was adjudged offside when replays demonstrated that the Brazilian might well have been level with the defender.
Both teams had bright moments in an entertaining second period, but it was Barcelona that looked the most likely as play developed. Dani Alves passed up a golden chance for the Catalan outfit, but Celta remained a threat down the other end with Hugo Mallo and Charles both coming close. Ultimately, Barca made the most of a set piece as Mathieu powered a header in off the crossbar to secure all the points. Celta can feel unfortunate, but the statistics show that they only managed one attempt on target all night, despite a number of excellent chances. A draw might well have been the correct result, but it is difficult to argue that Barca did not deserve all three points after turning the screw for long spells of the second half.
Celta were attempting to do the league double over Barcelona having won at the Camp Nou earlier this season and Eduardo Berizzo's side might feel that they will never get a better chance. As is often the case against the bigger teams, Celta were right in Barcelona's faces from the first whistle, with Michael Krohn-Dehli, Pablo Hernandez and Augusto Fernandez providing a support behind the front three of Larrivey, Orellana and Nolito. It was a bold selection from Berizzo and it almost paid off. As mentioned, Celta were the better team in the first period, but they could not find the back of the net despite a couple of excellent chances for Larrivey. It was always going to be the type of game where the first goal would be important and when Celta failed to take one of their many chances, Barcelona certainly grew in confidence.
It is difficult to be too critical of a Celta team that caused so many problems and were so solid at the back. Centre-back pairing Andreu Fontas and Gustavo Cabral both had excellent matches, while Nolito caused havoc with his movement in the final third. That said, despite Celta's pressure, they only managed one attempt on target throughout the 90 minutes. Statistics rarely paint a false picture, but the numbers do not do Celta justice. They gave Barcelona one of their hardest games of the season, but one lapse of concentration from a set piece allowed the visitors to claim all the points. The fact that Celta managed to tame Luis Suarez, Lionel Messi and Neymar, but conceded from a set piece will be really difficult to take.
Having watched Real Madrid thump Granada 9-1 in Sunday's early start, the pressure was back on Barcelona to regain a four-point lead at the top of the table and continue their excellent run of form in 2015. After what occurred throughout the match, head coach Luis Enrique might have been fairly pleased to take a point, but the Catalan outfit showed all the makings of a title-winning team by claiming a vital victory. In truth, Barcelona were really poor in the first period, with their attacking players struggling to make an impact in the final third and their defence looking shaky each time Celta broke the lines. Had Celta been a bit more clinical in front of goal then there is little doubting that the visitors would have been behind at the break. The international break appeared to take it out of Barcelona and last season, this would have been the type of match where they would have failed to collect all three points.
There is a sense of steel about this Barcelona team under Enrique, however, and they managed to claim a crucial win courtesy of Mathieu's second league goal of the season. A special mention must also be given to Gerard Pique, who was again sensational at the heart of the Barcelona defence. Further forward, Neymar had a shocker, while Messi and Suarez were also quiet on a night where Celta's back four came out on top. Winning titles is about finding ways to dig out results, however, and that was the case in Vigo. It is now 19 wins from their last 20 games in all competitions for the Catalan outfit, who are still on for a treble this season. Enrique will be pleased with the points here, but will want a stronger display next time out.
Sports Mole's man of the match
Gerard Pique: Celta's two centre-backs were both excellent, but Pique put on another near-perfect performance for Barcelona. The Spaniard made a host of super challenges as Barca struggled to contain Celta, with his standout moment occurring in the second period when he denied Charles, who was through on goal. Pique was criticised in the early part of the season, but he has been exceptional for some time now.
Messi was guilty of missing a golden chance for Barcelona late on, but that did not cost his team the points. Larrivey, however, will be left pondering what might have been. The Celta forward, who scored the winner at the Camp Nou earlier this season, had a wonderful opportunity to register late in the first half after being found by Orellana, but he fired high of the crossbar under little pressure. A goal at that stage might have produced a different result.
Referee Inaki Bikandi had a fairly busy night in Vigo. He issued just four yellow cards, but there were a number of incidents that the official had to deal with. Neymar registered for Barca early in the second period, but had the goal chalked off for offside when replays demonstrated that it was a close call. Bikandi's major contribution occurred late on, however, when he sent Orellana from the field for throwing a piece of turf at Sergio Busquets. It was a very bizarre incident and the referee might now have created a precedent for an incident that is not often seen in professional football.
Celta: Next up for Celta is a trip to Granada on Wednesday.
Barcelona: The Catalan outfit, meanwhile, welcome Almeria on Wednesday.