The Sweden striker dived full length to nod in a deflected Daniel Alves cross in the 82nd minute after teenage striker Bojan Krkic and Mali international Seydou Keita had put the European champions 2-0 ahead at the break.
With Argentina forward Lionel Messi on international duty, coach Pep Guardiola started with Pedro Rodriguez on the right wing, Ibrahimovic at centre forward and Bojan on the left.
The 19-year-old popped up unmarked to nod in at the back post in the 18th minute after Keita flicked on Xavi's corner, and Keita doubled the lead just before halftime when he headed home an Alves cross.
The match had been put back due to Barca's European Super Cup match against Shakhtar Donetsk in Monaco on Friday, which they won 1-0 with a goal at the end of extra time, and Guardiola had complained many of the players were feeling the strain.
"I can't complain about anything the team did as everyone was making an effort and everyone was running," he told a news conference. "We controlled the match."
Bojan and Brazilian left back Maxwell, who with Ibrahimovic joined from Inter Milan in the close season, were both substituted with injuries in the second half.
Barca said on their website Bojan had damaged a left leg muscle and would be out of action for 15-20 days while Maxwell's left leg injury needed further assessment.
"It was a difficult match in Monaco with extra time and that could have made things hard for us tonight," Keita, who also headed against a post in the second half, said on Barca TV.
"We just want to take each match as it comes and if we can be as successful as last year so much the better," he added.
In other La Liga matches at the weekend, World Player of the Year Cristiano Ronaldo converted a penalty to help Barca's arch-rivals Real Madrid beat Deportivo La Coruna 3-2.
Atletico Madrid were humbled 3-0 at Malaga, Valencia beat visiting Sevilla 2-0, and Villarreal surrendered the lead to draw 1-1 at Osasuna.
