Lionel Messi scored a hat-trick - his 35th - as the hosts fell apart after Ivan Rakitic's opener.
Diego Llorente and Manuel Iturra were both dismissed for Rayo, whose only goal was scored by Manucho.
Luis Suarez also had a penalty saved before Arda Turan completed the rout to move Barcelona eight points clear.
Atletico are second in La Liga, with Zinedine Zidane's Real Madrid 12 points behind the leaders in third.
Suarez's miss from the spot means Barcelona have failed to convert half of their 18 penalties this season.
Suarez's miss from the spot means Barcelona have failed to convert half of their 18 penalties this season.
