Lionel Messi's equaliser at Stamford Bridge last month ensured the last-16 tie headed to Camp Nou all square and Barca's all-time leading goalscorer nutmegged visiting goalkeeper Thibaut Courtois to fire his team ahead after three minutes.
Messi laid on Ousmane Dembele for a rasping second and scored his 100th Champions League goal when he got the better of Courtois once more after the hour.
Barcelona provided an object lesson in ruthlessness as Chelsea matched them for long periods in general play, hitting the post and the crossbar through Marcos Alonso and Antonio Rudiger respectively.
"We suffered a lot in this game because they were pressing really hard and creating a lot of danger," Valverde told a news conference, echoing the pre-match mantra of suffering voiced by opposite number Antonio Conte.
"They showed they were a great team with great players and we were lucky enough to knock them out.
"I have to admit they have been a great rival, a great team. It's been a very difficult tie, both legs.
"I think we scored with the first chance we had."
For giving his side that clinical edge, Valverde hailed Messi's peerless talent.
"That goes with Messi's personality, the sense of responsibility that he has," he said. "He knows in certain moments stars have to come out. He forces himself to do that.
"There's no guarantee that he's going to score but he is a fantastic player. We enjoy him.
"We're lucky enough to be seeing something that will go down in history."