The visitors arrived in Madrid unbeaten since 21 November, but were behind after six minutes when Lucas Vazquez headed home Marco Asensio’s cross.
Asensio got on the scoresheet himself in the second half when he sidefooted in from Casemiro’s pass.
Celta, who lost La Liga top scorer Iago Aspas to injury early in the second half, rarely posed a threat.
Santi Mina went closest when he swept a shot wide from the edge of the area.
Just 13 months after being shown the door at Tottenham Hotspur, Mauricio Pochettino is back in football at the highest level with French billionaires Paris St-Germain.
It was only ever going to be a tempting project at a massive club that would coax the Argentine back into the footballing limelight, and in that respect PSG fit the bill perfectly.
He spoke to many clubs during his enforced sabbatical, including Benfica and Monaco, and he was certainly approached and sounded out by Barcelona and Real Madrid, although no official offer was made.
But now the timing is perfect for Pochettino to take the reins at the Parc de Princes.
As a former player who enjoyed two and a half seasons at PSG, the decision to take the job may well be a no-brainer, but that’s a long way from saying it is going to be a walk in the park, as the former incumbent at the club Thomas Tuchel would no doubt tell him.
Tuchel had already told the club he wasn’t going to be staying on next season.
Tuchel is one of those modern German managers who has always understood football as a game in which the collective is far more important than the individual, whereas at a club like PSG the importance of the star is paramount, to the extent that players like Kylian Mbappe and Neymar have a direct line of communication with the president.
Unsurprisingly therefore, you sense Tuchel felt his authority was being constantly undermined.
Despite being runners-up in last year’s Champions League, he leaves with the club – French champions in seven of the previous eight seasons – in a recently unprecedented third place in Ligue 1.
They are still just a point off top spot and very much in with a chance of winning the league, but it is their worst return at this stage since the 2013-14 season.
Fourteen points from a possible 24 might be good enough at any other club, but Tuchel leaves with PSG having lost four of their first 17 games.
Last season, before the league was terminated after 27 games, they had lost just three. But the sacking had more to do with perception than numbers.
The main focus of the squad last season had been on the Champions League and they followed his instructions to the letter.
During that campaign they showed unity particularly when, after a dinner at Marco Verratti’s restaurant where they promised to work as a team, they came back from a 2-1 first-leg deficit against Borussia Dortmund to win the home game 2-0 and make their way into the quarter-finals just before the pandemic hit.
But this season it has proved impossible to recreate that spirit and the often tetchy and awkward relationship Tuchel had with director of football Leonardo meant he had to go.
Mauricio Pochettino guided Tottenham to their first Champions League final, losing 2-0 to Liverpool in June 2019
Pochettino, meanwhile, has been playing the waiting game. It hasn’t been the easiest of times for him, although he knew that sooner or later an opportunity would appear.
He has been to Qatar following an invitation from the supreme committee of the World Cup, and a lot of players who see him very much as a wise counsel have been in contact in search of support.
Former players who are trying to get their coaching badges and coaches who are on a break have been in touch, aware that this is a special manager who can bring the best out of the players he has by getting into their heads and working on establishing a personal relationship.
Because of that crucial element, he spent much of his time working on finding a way of dealing with the new generation of players, which is very different to dealing with the veterans of a side.
He has been invited into chats both privately and in groups. He has had Zoom conversations with Argentine coaches, and he has also been watching a lot of football, evaluating players and coaches and coming to the conclusion that, as things stand, while the industry may be the same one, the game post-Covid most certainly isn’t.
Pochettino has no agent, no PR man organising his schedules, and the Pochettino team deal directly with both the media and the clubs that are interested in talking with them.
Since last Christmas they could have been working almost non-stop, and there has been some carefully selected media work done in the interim.
Numerous offers to do advertisements came his way, but he turned them all down, partly because he does not feel comfortable doing them and also because he is aware that in his next club there will be advertising commitments, and he wanted to avoid any possible conflict of interest.
They also take energy away from his main focus – improving his methods and his team. That is why he is not involved in social media.