Coming into this fixture, Rayo had scored the opener in each of their last four head-to-head's, and they repeated the trick here, netting after just nine minutes.
The home side were rewarded for their energetic start, placing Barcelona on the back foot as Unai Lopez swept a Jorge de Frutos cut-back inside Marc-Andre ter Stegen’s near post.
There were several flare-ups during a competitive half, but in terms of goalmouth action, chances were limited.
Lamine Yamal had the visitors’ best opportunity before the break, with his swerving strike testing Daniel Cardenas in the latter stages of the half.
Looking for an instant impact, Hansi Flick introduced summer signing Olmo at half-time for his Barca debut. That substitution seemed to provide fresh impetus, as just five minutes into the half, Barcelona were inches from levelling the scores when Raphinha’s zipped pass across goal narrowly evaded the touch of a sliding Robert Lewandowski.
Rayo were then almost caught off-guard minutes later thanks to Olmo’s speculative long-range effort that rattled the crossbar.
At this stage, an equaliser looked inevitable, and it duly arrived on the hour mark.
A give-and-go between Pedri and Raphinha ended with the former tucking in his first goal of the season with a neat finish, setting up an exciting final half-hour.
Barcelona continued to push for goals, and after a further 11 minutes of Rayo resistance, it looked as if Lewandowski had found it, but his close-range finish was chalked off for a foul in the build-up.
Time was ticking away for Flick’s men, yet the near-constant pressure eventually paid dividends as Olmo superbly controlled Yamal’s pass before picking his spot in the bottom corner, handing his side a deserved lead.
A much improved second-half display ultimately secured the win for the visitors, taking them to nine points after the first three games in La Liga. Coincidentally, Barcelona have now scored exactly two goals in each of their last six away league matches, failing to keep a clean sheet in five of those games.
For Rayo, a solid performance counted for little in the end; it’s just a third defeat in seven home league matches for Los Franjirrojos – a spell that spans back to the end of last season.
Flashscore Man of the Match: Raphinha (Barcelona)
