Ousmane Dembele's strike sent Barcelona three points clear at the top of La Liga with a tense 1-0 win over Atletico Madrid on Sunday.
Capitalising on champions Real Madrid's defeat by Villarreal, Barcelona set out to make a statement victory at the Metropolitano.
Shorn of suspended top scorer Robert Lewandowski, Xavi selected Ansu Fati up front in his place, but it was Dembele who made the difference, finishing a slick move in the 22nd minute.
Atletico ramped up the pressure, with the superb Ronald Araujo clearing off the line from Antoine Griezmann at the death, but Diego Simeone's side could not find an equaliser.
Both teams finished with 10 men after Ferran Torres and Stefan Savic were sent off for brawling with each other on the floor as tempers soured.
Defeat means Atletico languish in fifth, 14 points behind leaders Barcelona.
"We are very happy, we knew it was a difficult place to go, that Real Madrid had slipped up and it was a chance we had to take," Barca midfielder Sergio Busquets told DAZN.
"Although they came out strongly in the second half, we knew how to control the game. In the end we suffered, but these are three very good points."
Barcelona have conceded just six goals in their first 16 La Liga matches but Griezmann twice came close to finding the equaliser Atletico craved.
The Catalans only mustered two shots on target and Atletico goalkeeper Jan Oblak said his side deserved more.
"We had a good game, apart from the first 25 minutes," Oblak told DAZN.
"We pressed well, we had chances, but lacked a bit of luck to score. I think that we had a good game generally and we could have scored, but the ball didn't go in.
"We started badly, the first 25 minutes we had little confidence, and later we woke up, but at 1-0 down it's already harder."
- Decisive Dembele -
Youngster Fati had an early effort brilliantly blocked by the sprawling Jose Gimenez, as Barcelona dominated the opening exchanges.
The coach opted to play with four midfielders instead of his usual three, starting with both Sergio Busquets and Frenkie de Jong as well as youngsters Pedri and Gavi.
Xavi said on Saturday Atletico barely have any gaps in their defence but Pedri uncovered one to create the opening goal.
The midfielder burst forward in the 22nd minute to capitalise on space in front of the box, before feeding Gavi, who teed up Dembele to clinically slot home.
Pedri could have doubled the lead moments later when Atletico foolishly gifted him the ball with a poor pass-back, but he delayed his finish too long and Nahuel Molina denied him.
Marcos Llorente had Atletico's first decent opportunity after half an hour when Griezmann scooped a ball delicately over the defence to set him in, but Araujo deflected his effort into the side netting.
Gimenez headed narrowly wide with Marc-Andre ter Stegen rooted to the spot as the hosts began to wrestle back control.
The German goalkeeper made a superb save at full stretch to deny the pink-haired Griezmann, who was becoming increasingly influential against his former side.
Griezmann whipped a strike high over the crossbar as Atletico began the second half in determined fashion, pushing Barca deeper and deeper.
Only his compatriot Dembele offered the leaders an outlet on the break and he had a drive deflected into the side-netting.
Xavi brought on Franck Kessie for De Jong and it helped steady the ship, with Barcelona managing some stretches of possession which frustrated the home fans and took the sting out of the game.
Red cards for Torres and Savic reignited the game in stoppage time and Griezmann might have snatched a point for his team but for Araujo's crucial clearance on the line.
The victory earns Xavi some breathing room after criticism and fills Barcelona's sails with wind ahead of the imminent Spanish Super Cup in Saudi Arabia.