Earlier Atletico Madrid were hammered 3-0 by Valencia at Mestalla with coach Diego Simeone labelling it the "weakest" performance during his time at the club.
Barcelona played with a vibrancy they lacked at times last season, even as they lifted La Liga, warming up for their Champions League opener on Tuesday against Royal Antwerp.
Xavi handed Felix and compatriot Cancelo their first starts for the club and they quickly impressed home fans and their coach.
"We're talking about two players there are absolutely no doubts about in terms of individual quality," Xavi told reporters.
"The two bring something different that improves the team. Individual quality is what makes the difference."
Betis, lining up with a back four composed only of former Barcelona players, played with attacking intent, unlike many other teams who will visit the temporary Olympic Stadium home of the Spanish champions.
However Barcelona moved ahead after 25 minutes when Oriol Romeu fed Felix.
The on-loan Atletico forward controlled the ball, knocked it past goalkeeper Rui Silva and then squeezed home clinically from a tight angle.
"I'm very happy to be starting again, the feelings are very good -- it's easy to play in this team," Felix told Movistar.
Felix, signed by Atletico Madrid for a club record fee of 126 million euros ($134 million) in 2019, failed to find consistent form in the capital and was loaned to Chelsea last season.
"I am happy, the change has done me good, me and my family, I am very happy here," he added.
Lewandowski doubled Barcelona's lead when he ran onto Andreas Christensen's pass and slotted home, but the goal was crafted by Felix, whose clever dummy allowed the ball to find the Polish striker.
- The 'shark' bites -
Torres, selected ahead of teen starlet Lamine Yamal, netted the third, with a low free-kick around the wall -- the first Barcelona have scored since a Lionel Messi strike in May 2021.
The winger, who has nicknamed himself a "shark" since the summer after working on mental aspects of the game and finding his best level of fitness, celebrated effusively.
"I didn't know we hadn't scored a free-kick since Messi," said Torres.
"I have a lot of confidence, I am working on it and I'll keep doing that."
Raphinha, who replaced Torres, quickly added the fourth just moments after entering the fray with a drilled effort from outside the area into the bottom corner.
Cancelo gleefully added the fifth to cap an excellent individual display, skinning former Barcelona left-back Juan Miranda and driving home across goal.
Whether new-look Barcelona can match Europe's best remains to be seen but this rampant display highlighted the improved attacking quality at their disposal this season.
- 'Weakest game' -
Atletico coach Simeone said his team put in their "weakest" performance of his 12-year reign in their three-goal thrashing by Valencia.
Hugo Duro netted a brace for the hosts and Javi Guerra tucked home the third as they dominated.
Los Che have started the season well after flirting with relegation until the final day of the previous campaign, and this was their finest outing yet under coach Ruben Baraja.
"We had the weakest game since I arrived at the club, and we have to congratulate our opponents," said Simeone.
Defeat was the worst way for Atletico to prepare for the start of their Champions League campaign on Tuesday at Lazio.
"They came into the game with a lot more intensity and if you don't match it ... it's impossible to win any game," said Atletico goalkeeper Jan Oblak.
"We have to look in the mirror. We know we can give a lot more than we gave today."