With new president Josep Maria Bartomeu watching on from the directors’ box, Gerard Pique swept home the opener from Xavi’s corner five minutes before half-time.
Pedro Rodriguez then made the game safe with a neat turn and finish from Lionel Messi’s pass ten minutes after the restart.
Alexis Sanchez slotted home the third moments later from Pedro’s cross for his 12th goal of the season.
However, it was to be another frustrating evening for Messi in front of goal as his La Liga goal drought stretched to eight games but victory ensured Barça continued their record run of finishing top of the table for 59 consecutive rounds of league games
David Villa put the visitors in front after just eight minutes with his 11th goal of the season, but Diego Simeone’s men were thankful to goalkeeper Thibaut Courtois moments later as he saved Jonathan Viera’s penalty.
Arda Turan doubled Atletico’s advantage at the end of a fine team move involving Diego Costa and Jose Sosa before Viera’s deflected strike had briefly given Rayo hope.
The visitors restored their two-goal cushion before half-time, though, as Turan slotted home Gabi’s free-kick from a tight angle at the back post.
Saul Niguez’s then put through his own net under pressure from Costa to make it 4-1 before Joaquin Larrivey’s headed consolation rounded off the scoring.
With top-scorer Costa still to score in seven games in 2014, Villa’s return to goalscoring form has come just at the right time and he slotted away the opener confidently from Costa’s unselfish cut-back.
Elsewhere, Athletic Bilbao also enhanced their chances of playing UEFA Champions League football next season with a crushing 5-1 win over Osasuna to move five points clear of Villarreal in fourth. In Sunday’s early game, Almeria took down Getafe 1-0, with Sundy Jonathan scoring four minutes after the break.