It wasn’t the perfect evening for City, which is bidding to become the first team in English soccer history to win four straight top-flight league titles.
Kevin De Bruyne, starting for the first time since coming off early in the Champions League final with a hamstring problem, lasted 23 minutes before needing to be substituted after pulling up.
Guardiola said it was a recurrence of the same problem.
“It’s a pity — he has recovered well but now we have lost him for some time,” Guardiola said.
Also during the first half, City defender Rico Lewis was struck by a lighter thrown from the crowd as he lay on the ground near the corner flag after being fouled. Burnley said a fan had been removed from the stadium by police in an incident that further ruined its return to the Premier League after one season away.
Haaland gave City the lead with his first touch in the game when he latched onto Rodri’s nod-down from De Bruyne’s right-wing cross and sidefooted a finish into the bottom corner.
His second goal was more spectacular and came after Julian Alvarez laid off a cross from Kyle Walker. With his back to goal, Haaland sent a first-time shot on the turn off the underside of the crossbar and into the top corner.
Haaland was without a goal in his last six matches for City, including the loss to Arsenal in a penalty shootout in the Community Shield on Sunday.
“I just have to keep on working, keep relaxing and not to focus on negative things,” Haaland said.
Rodri, who scored City’s winner in the Champions League final against Inter Milan in June, smashed home the third goal from close range in the 75th minute after Burnley failed to clear a free kick into the area.
Burnley ended the game with 10 men when Morocco winger Anass Zaroury was shown a straight red card for a dangerous tackle on Walker deep into second-half stoppage time. The referee initially gave a yellow card but upgraded it after viewing the pitchside monitor.
City, which gave a debut to centre-back Josko Gvardiol as a second-half substitute, next plays Sevilla in the UEFA Super Cup on Wednesday. It’s a match between the winners of last season’s Champions League and Europa League.