Pep Guardiola's side started the day under pressure lying third in the table and appeared to be weakened when Lionel Messi and Zlatan Ibrahimovic were not in the team.
Any worries were quickly dispelled though, Pique volleying home from a 10th-minute corner and Pedro doubling the advantage after a flowing attacking move 16 minutes later.
"Obviously I feel happier with Ibra and Messi on the pitch but there was a risk I would lose them for a long time," said Guardiola.
"I have to congratulate the team for the way they played. It's a great risk to attack the way we did with Samuel Eto'o and Diego Milito against you but it would have sent a bad message to my team if we had changed the way we played."
Inter were on the back foot and Barca extended the lead after a typically slick interchange of passes.
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Daniel Alves was played in off the right flank and crossed to the back post where Pedro's weak volley beat Inter goalkeeper Julio Cesar.
Jose Mourinho's side showed more intent after the break but it was Julio Cesar who was called into action again, saving one-handed from Xavi's angled header.
Inter striker Eto'o, who left Barca as part of the swap deal that took Ibrahimovic in the opposite direction, was given a warm reception by the home fans but had few chances to mark his return with a goal.
"There's little to say about the game. The best team won," Mourinho said.
"Unfortunately we were without (injured playmaker) Wesley Sneijder. Messi and Ibrahimovic are good players but Barca have replacements. We don't have another Sneijder."
