The pair were directly responsible for every goal scored by the Blaugrana, who maintained their seemingly unassailable 13-point lead at La Liga's summit
Lionel Messi struck twice to extend his incredible scoring streak to 18 consecutive league games, but it was his understanding with David Villa that was the highlight of the match, with both players dispelling rumours of a rift to combine for all three of Barca's goals.
Villa got the ball rolling 25 minutes in by confidently slotting home a pass from Messi, who himself slid in the second five minutes before half-time after latching onto the Spain striker's through ball.
The Argentine would clip home a brilliant third shortly after the hour mark, though Barca were not able to hold onto their clean sheet when Raul Tamudo poked home a consolation for Rayo with 20 minutes to go.
Nevertheless, with only 10 games to go in the Liga season, the win sees the Catalan giants re-open their 13 point lead at the top of the table over second placed Real Madrid.
Jose Pinto deputized for the suspended Victor Valdes in goal, while Javier Mascherano started in defence in place of injured captain Carles Puyol.
Perhaps inevitably, it was Messi at the end of the first chance of the game, when the Argentine crashed a free-kick agonisingly off the crossbar with six minutes gone.
Rayo though did not seem fazed by the calibre of their opponents, and began the match brightly, matching the passing output of the Catalans with some impressive possession of their own.
But the visitors could not find a cutting edge to match their control of the ball, which would end up costing them when a sweeping counterattack saw Messi drive half the length of the pitch before slipping in Villa for an emphatic finish.
The goal seemed to spark Barca further into life, and as the first half wore on, Rayo’s influence faded as the tiki-taka football of the home side got into full flow, despite Adriano trudging off for Dani Alves due to injury.
And five minutes before the break, the Messi-Villa axis would carve them apart again, as the latter took his time to find the overlapping run of the former, who slotted a first-time finish into the bottom corner.
The home side did not let up in the second half, and nine minutes after the restart, Alexis Sanchez came close to adding a third when he fired narrowly wide after a slick move involving Dani Alves and Messi.
But the third goal was always coming, and it arrived via the same two players that had tormented Rayo all game long. Villa did well to harness a long ball and spread to Messi, who bulldozed past Anaitz Arbilla and clipped delicately over Ruben Martinez.
Rayo would finally have something to cheer with 20 minutes to go, when substitute Tamudo ghosted into the six-yard-area to turn home a low cross from Piti.
But the visitors were soon indebted to Martinez in goal for tipping over a stinging drive from Messi, who was certain that he had sealed his hat-trick.Still, Rayo had two late chances to make it interesting, but Tamudo drilled wide in a carbon copy move from his goal, while Piti's long-rang drive was saved by Pinto as Barca avoided an awkward end to the game.