Raphinha and Lamine Yamal both scored twice, while Rayo defender Florian Lejeune put through his own net as Hansi Flick's side secured a third consecutive league victory.
Rayo strike first, but Barcelona respond
Rayo stunned the home crowd after Sergio Camello opened the scoring in the 12th minute, finishing from an Álvaro García cut-back.
Barcelona, however, responded almost immediately.
Raphinha equalised in the 19th minute, cutting inside before firing a low shot beyond Dani Cárdenas.
Just two minutes later, Lamine Yamal completed the turnaround with a superb left-footed strike from the edge of the area to put Barcelona 2-1 ahead.
The hosts dominated the remainder of the first half, finishing the opening 45 minutes with 73 per cent possession and 17 attempts, compared with three from Rayo.
Barcelona extend their advantage
Barcelona increased their lead six minutes after the restart when Florian Lejeune turned the ball into his own net, making it 3-1.
Rayo refused to surrender, though, and Camello scored his second of the evening in the 59th minute, heading home from a corner to reduce the deficit to 3-2.
The visitors briefly threatened to draw level, but Barcelona regained control.
Raphinha strikes again
Raphinha restored Barcelona's two-goal advantage in the 71st minute, finishing after an excellent assist from new signing Anthony Gordon.
The goal was particularly significant for the Brazilian, who moved to five goals in the opening three league matches, making him LaLiga's leading scorer at this stage of the campaign.
Gordon also continued his impressive start, registering his third assist in three LaLiga appearances.
Yamal completes the rout
Barcelona saved the best for last.
In the 90th minute, Lamine Yamal scored his second of the night, cutting inside before curling a precise left-footed effort into the bottom corner to complete the 5-2 victory.
The result gives Barcelona nine points from their opening three matches, keeping them level on points with Real Madrid at the top of the LaLiga table, with Barcelona ahead on goal difference.
Match facts
Barcelona will now look to carry their perfect league record into their next fixture against Valencia on September 6.