Barcelona fought back to beat Atletico Madrid 4-2 in a LaLiga thriller at the Camp Nou on Sunday as it clinically saw off the champions by scoring four goals from its only four shots on target in the game.
A rampant Barca scored four goals in 40 minutes at Camp Nou before surviving a late fightback from Atletico after Luis Suarez headed in against his former club and Alves saw red with 20 minutes left.
Real Madrid then capitalized on Sevilla's goalless draw with Osasuna on Saturday by edging past Granada 1-0 to extend its lead at the top of the table to a daunting six points.
In the absence of the injured Karim Benzema, Marco Asensio finally broke Granada's resistance in the 74th minute at the Santiago Bernabeu.
A statement victory returns Xavi Hernandez's into the top four for the first time since September, with Atletico now two points behind in fifth.
Atletico took an early lead through Yannick Carrasco but Barcelona came storming back, Alba equalizing with surely one of the goals of the season before Gavi, Ronald Araujo and Alves all struck to leave Atletico facing an annihilation.
Instead, Suarez headed in and Alves was sent off as tempers flared. But Barcelona held on, with Pierre-Emerick Aubameyang, signed from Arsenal, coming on off the bench to make his debut in the second half.
With Barcelona in containment mode, Aubameyang's influence was limited and it was another January signing, Adama Traore, who made the biggest impact with an electric first-half performance.
Barca was ninth in the league, six points behind Atletico in fourth when Xavi was appointed coach.
Now, it is in the driving seat to seal qualification for the Champions League, which would be so crucial to its financial recovery.
Barca came into the game on the back of a dramatic transfer window that also saw Ferran Torres brought in.
Traore, a La Masia graduate, and Torres both started but Aubameyang, who had been sidelined by Arsenal in recent weeks, was only deemed fit enough for the bench, along with Ousmane Dembele, who Xavi welcomed back into the fold despite threats of exile last month from the club.
Dembele is yet to extend his deal, which expires in the summer, and he was whistled before kick-off.
He was not introduced in the second half, although such was the drama of the contest by then, perhaps the crowd might not have noticed.
Atletico was ahead on eight minutes but the rest of the first half belonged to Barca.
Traore was at the heart of it, making the game his own for a whirlwind half an hour.
He pressed and harried and terrorized Atletico, until Simeone even had to bring Carrasco over from the right for cover.
Traore was involved in Alba's equalizer too, his cross poked out to Alves, who floated the ball to the opposite side, where Alba had time to adjust his feet and let fly with a stunning volley. The ball flew over Jan Oblak and into the far corner.
Barcelona was on top and Traore was in full flow. He stopped Mario Hermoso, then surged past him, lifting a cross off the line and into the area where Gavi headed in a second.
Pedri should have made it three but fired over and as Atletico hoped for halftime, Barcelona struck again, Alves' chip headed onto the crossbar and the ball bouncing up for Araujo to smash in.
Four minutes after the restart, Barca made it four, Gavi's cut-back finding Alves, who arrowed a finish into the corner. Alves milked the celebration, posing with his arms outstretched after his first Barca league goal since 2013.
But the party atmosphere was popped when Suarez reduced the gap to two by heading in from close range.
Aubameyang briefly broke the tension by coming on to rapturous applause for Traore but Alves was then sent off after scraping his studs down the back of Carrasco's leg.
Atletico had 20 minutes to score two and the game almost boiled over when Xavi's assistant Oscar Hernandez was shown a red card for his protests and Xavi saw yellow.
A third for Atletico and Barcelona might have caved but it never came.
Granada looked like it might hold on against Real Madrid, who was without its deadly attacking duo, Vinicius Junior suspended and Benzema still recovering from a thigh strain.
Isco and Rodrygo started up front instead but were replaced by Luka Jovic and Eden Hazard shortly before Asensio struck, a superb, swerving shot finding the corner after Eder Militao had won the ball back.
