After being put under pressure in the first half-hour, Barcelona opened the scoring in the 38th-minute through Atletico loanee Joao Felix.
Robert Lewandowski subsequently produced an exquisite finish in the opening stages of the second period, before Fermin Lopez added a third just after the hour mark to leave Atleti with a near-impossible challenge.
Matters got worse for the hosts when Nahuel Molina was given his marching orders in stoppage time for fouling Vitor Roque as the last man.
The late dismissal summed up a disappointing evening for the hosts, who fell to their first league defeat at the Civitas Metropolitano since losing 1-0 in their previous home clash with Barcelona in January 2023.
The victory moves Xavi's side above Girona and into second position, while fifth-placed Atleti are left sitting one point adrift of Athletic Club in fourth spot.
Both teams entered the crucial La Liga meeting in high spirits after they both eliminated Italian opposition in midweek to secure their spots in the Champions League quarter-finals.
However, Barcelona did receive a setback before the first whistle, with Andreas Christensen dropping out of the starting lineup after feeling discomfort in the warm-up.
The eleven Barcelona players that made it onto the pitch were forced to weather an early storm from their determined hosts.
Atleti went close to taking the lead in the seventh minute when Rodrigo De Paul won the ball back on the edge of the box before teeing up Pablo Barrios, who fizzed his effort just wide of Marc-Andre ter Stegen's left post.
After surviving Atletico's period of dominance, the visitors started to grow into the contest as the first half wore on.
Fermin, who replaced Christensen in the lineup, had Barcelona's first meaningful chance of the contest, latching onto Pau Cubarsi's long pass before firing straight at Jan Oblak at the near post.
After failing to take heed of Fermin's warning shot, Atleti were ultimately punished just moments later when Felix turned the ball home from Lewandowski's neat cut-back to score against his parent club for the second time this season.
Alvaro Morata then spurned a chance to score an immediate equaliser, lifting his shot over the bar after pouncing onto a loose ball.
With his team trailing at the break, Diego Simeone turned to his bench, introducing the attacking qualities of Antoine Griezmann and Memphis Depay.
Unfortunately for the hosts, Barcelona doubled their advantage through Lewandowski before either Griezmann or Depay had the time to make an impact.
The Poland international took the ball away from goal with his first touch from Raphinha's through ball, but he still managed to showcase his clinical nature in the final third to swivel and fire in off the far post.
Ter Stegen then backed up Lewandowski's 13-league goal of the season by making a superb diving stop to prevent Marcos Llorente from halving the deficit.
As the contest moved into the final half-hour, Barcelona carved out a third goal to effectively put the game to bed with plenty of time to spare.
Kounde's inviting delivery from the right flank found the unmarked Fermin, who calmly nodded past the helpless Oblak to net his third La Liga goal of the campaign.
While the fate of the three points was decided, Saul Niguez still spurned a golden opportunity to register a late consolation, dragging his left-foot strike harmlessly wide from inside the Barcelona box.
Atletico's miserable evening was compounded when Molina received a red card for hauling down Roque just as the Brazilian was set to race into the box and unleash a shot.
The win helps Barcelona tighten their grip on a top-four spot and moves them back to within eight points of leaders Real Madrid.
The Blaugrana will return to action against Las Palmas after the international break, while Atleti will face Villarreal in an away fixture on April 1.