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.
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.