The Chile international surpassed 560 minutes without conceding in La Liga as Luis Enrique's side took advantage of Atletico Madrid's defeat
Luis Enrique's side suffered a 3-2 defeat at Paris Saint-Germain in Tuesday’s Champions League clash, but Rayo offered no such threat as Claudio Bravo surpassed Pedro Artola's record of not conceding during the first 560 minutes of a Liga season.
Although the home side enjoyed a lively start on Saturday, Barca's record of averaging four-and-a-half goals in their last seven meetings with Rayo was not an encouraging omen.
And eventually Barca found their stride, as Lionel Messi opened the scoring just after the half-hour, with Neymar following suit shortly afterwards.
Rayo improved again after the break, yet their chances of salvaging an unlikely draw slipped away following Jorge Morcillo's 60th-minute dismissal.
In truth, the scoreline should have been much more dominant in Barca's favour, and Javier Aquino also saw red to cap a frustrating outing for the Madrid club.
Luis Enrique was adamant that, despite Barcelona's excellent record against Rayo in recent seasons, Paco Jemez's side would provide a stern test for his team in Vallecas.
And Rayo seemingly proved the 44-year-old's point early on, as Bravo was forced into a fine save down to his right to deny Alberto Bueno's goal-bound effort.
After making that save, Bravo remained untested until he finally clinched his clean-sheet record in the 21st minute and that appeared to let Barca relax, as their dominance began to grow.
Messi correctly saw a goal disallowed for offside in the 31st minute, but he would not be denied by anyone a few moments later, as he raced on to Gerard Pique's pass and lifted a delightful finish over Tono.
Rayo did not know what had hit them and they found themselves even further behind in the following minute.
Munir El Haddadi played Neymar in on goal and the Brazilian fired across the goalkeeper from the edge of the area to open up a handsome lead.
Teenager Munir caused problems again just before the break as he was tripped by Tono, yet no penalty was awarded.
Jemez introduced Aquino and Manucho at half-time and they appeared to have a positive impact, as Rayo became more potent in the final third.
Leo Baptistao almost brought Rayo back into the contest in the 58th minute, testing Bravo with a fierce effort from the right side of the area as the hosts continued to improve.
But just a few moments later, Rayo's uphill battle became even more perilous as Morcillo picked up his second yellow card for catching Neymar late.
Rakitic, a second-half substitute, nearly netted a third for Barca in the 71st minute as he shot straight at Tono from close range, while Messi wasted a glut of late openings to add gloss to the scoreline.
Aquino's hard tackle on Sergio Busquets earned Rayo's second red of the game in stoppage time as Barca saw the game out to keep their place at the top of La Liga, with Bravo reaching the 630-minute mark unbeaten as the final whistle sounded.