Lionel Messi scored the 24th hat-trick of his La Liga career as rampant Barcelona went to the top of the table.
Barca took full advantage of Real Madrid's defeat by Athletic Bilbao as Luis Suarez also scored twice.
Suarez fired the hosts ahead and Gerard Pique forced in the second before Messi netted three in eight minutes.
He scored a twice-taken penalty, tapped in the fourth and added a classy fifth before Suarez wrapped it up after an Alberto Bueno penalty for Rayo.
Both sides finished with 10 men as Román Triguero collected a second yellow card for pulling down Suarez, conceding the penalty that allowed Messi to make it 3-0.
Barca defender Dani Alves was then dismissed 10 minutes from the end for tripping Bueno as he went through on goal.
The Rayo striker took the penalty himself to move to 13 La Liga goals for season.
Messi now has 30 league goals, the same total as Real Madrid forward Cristiano Ronaldo, whose tally of 23 La Liga hat-tricks now trails Messi by one.
The 27-year-old Argentine, now also holds the record as the most prolific hat-trick scorer in Spanish football, with his 32 in all competitions eclipsing the total he previously shared with Telmo Zarra, who played most of his football for Athletic Bilbao from 1940-55.
Messi clocked up his latest record figures despite an anonymous first-half performance against mid-table Rayo, whose goalkeeper Cristian Alvarez produced an inspired performance to limit the damage.
Suarez opened the scoring with his 12th goal of the season after five minutes, steering the ball home from Xavi Hernandez's fine pass.
But after Pique had made it 2-0 early in the second half, following up after an Alves header had hit a post, Messi took over.
After his initial spot-kick was saved, the Argentina international was given a second opportunity because of encroachment into the penalty area and he drilled the ball home.
His second was a tap-in after a Suarez shot had been saved by Alvarez before a trademark shimmy took him round the Rayo goalkeeper to give him his 41st goal of the season in all competitions.
Barcelona are now one point ahead of Real Madrid and the two sides meet at the Nou Camp on 22 March.
