After they fell behind in the 15th minute, Neymar won and converted a pair of spot kicks and added two more goals in the second period before teeing up Luis Suarez to score a fifth for the home side late on.
He is the first Barca player other than Lionel Messi to score four in a match since Samuel Eto'o in 2008 and his eight goals in La Liga this term are helping offset the impact of Messi's absence through injury.
One piece of skill particularly caught the eye on Saturday when Neymar feinted to go one way and tapped the ball through the legs of Nacho before the Rayo defender stuck out a leg and felled the Brazilian to concede a spot kick.
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"I can't explain how I do things, it would be giving away clues," Neymar told Spanish television when asked about his brilliant move.
"It all comes from practising many times," he added.
"I am very pleased with the win and for how we played. Rayo are a great team and it cost us a lot to beat them."
Neymar's fine run of form is good news for Barca ahead of their Champions League Group E game at BATE Borisov on Tuesday.
His four-goal haul was the fifth of his career following two for Santos and two for Brazil and he tops the La Liga scoring chart ahead of Real Madrid forwards Cristiano Ronaldo and Karim Benzema, who each have six.
Barca's victory put the champions level on 18 points with Real after eight matches, although Villarreal can reclaim top spot with a win at home to Celta Vigo on Sunday.
(Reporting by Iain Rogers, editing by Ken Ferris)
