Barca were confirmed as champions on Saturday night when Real Madrid could only draw at Espanyol, and they showed their class by coming from behind to beat Atletico in a game that was soured by an injury to Lionel Messi.
It looked like they would mark the occasion with defeat as they trailed to Radamel Falcao's opener when Messi limped off on 67 minutes.
But by the time their talisman had reappeared, changed and showered, on the touchline Barca had snatched an away win.
Alexis Sanchez equalised on 72 minutes, following a one-two with Cesc Fabregas, before Gabi awkwardly turned a David Villa shot into his own net nine minutes from the end.
Valencia kept the pressure on Real Sociedad for the final Champions League spot by thrashing Rayo Vallecano away from home.
Roberto Soldado scored twice before the break, while Andres Guardado and Nelson Valdez completed the rout in the second half.
As speculation continues over Manuel Pellegrini's future at Malaga and a possible switch to Manchester City, his side played out a goalless draw with Sevilla.
The two sides were evenly matched and although Sevilla created marginally the better chances, a draw was not an unfair result in the end.
The result all put paid to Malaga's already slim hopes of finishing in the top four, as they are five points behind Valencia with one game less to play, while it also does little to boost Sevilla's European hopes.
Real Betis boosted their European hopes after ending a four-match winless run with a 1-0 triumph over relegation-threatened Celta Vigo.
Ruben Castro's goal midway through the second half decided things in Betis' favour as they kept the heat up on stuttering Malaga.