Sergio Camello's early opener for Rayo Vallecano threatened to derail a perfect start to the season, but Barcelona responded within two minutes through Raphinha and Lamine Yamal, and a Florian Lejeune own goal extended the lead before the break.
Camello pulled one back with a second headed goal shortly after the hour, but further strikes from Raphinha and Lamine Yamal, either side of Rodri's introduction from the bench, sealed a 5-2 win that kept Barcelona top of the table with a perfect record after three matches.
Hansi Flick was pleased with his side's opening period.
"In the first half we played fantastically. We had a good reaction to the goal, which is something that could happen," he said. He wants more control once games are established, though.
"At home we have to control the match better. Have more of the ball. It's in our mentality, some of the players want to go forward and attack, but sometimes it's necessary to slow the game down."
That theme extended to his assessment of Rodri, introduced midway through the second half.
"Rodri is here to control the game at certain moments. He needs to improve because he's only been with us a few days," Flick said. "We need to control things more because the opponent is very good and has a lot of players who know how to find space. They're also good from set pieces."
Asked about Gabriel Jesus, who watched from the stands ahead of his imminent unveiling as a Barcelona player, Flick was enthusiastic.
"Gabriel is a top-class forward. He can bring us a lot," he said. "He was coming back from injury, and I think he's fine. I spoke with him this afternoon — he was surprised. I like his style, how he plays... it fits our style. It's a great signing, Deco has done a fantastic job."
On the result itself, Flick pointed to the bigger picture.
"What matters is the three points. We've started the season well," he said, adding that his side must improve their ball recovery in open play. Asked whether more transfer business was likely before Tuesday's deadline, he played it down: "I don't know if there'll be more movement, I don't think so. But we'll see."
Raphinha's brace took his tally to five goals for the season, and Flick had no doubts about his captain's form.
"Of course I expected his performance, he's a world-class footballer. I always want him in my team, and being captain is good for him," Flick said, also praising the impact of debutant substitutes.
He was similarly effusive about Lamine Yamal: "I'm very happy with him. The way he plays... it's incredible to watch. He's at an incredible level."