Rodri completed the scoring after Haaland's first-half double to give City a perfect start to their quest to become the first side to win four consecutive English top-flight titles.
Haaland fired City to a treble of Premier League, Champions League and FA Cup glory last season by scoring 52 times in his first year at the club. The 23-year-old took just over three minutes of the new campaign to open his tally once more when he swept home Rodri's header across goal.
Haaland then crashed in a shot off the underside of the bar nine minutes before half-time as his finishing papered over the cracks of a far from perfect first 45 minutes from the visitors.
But the ease with which Pep Guardiola's men cruised to victory after the break was an ominous sign for the chasing pack aiming to dethrone City. Rodri completed the scoring when the Spaniard smashed home a loose ball from a free-kick 15 minutes from time.
City's night, though, was soured by an injury to captain Kevin De Bruyne. The Belgian had only recently returned from a hamstring tear he suffered in the Champions League final and limped off midway through the first-half.
Burnley boss Vincent Kompany has a statue outside City's Etihad Stadium in honour of his decorated playing career with the English champions.
Kompany returned the Clarets back to the Premier League at the first time of asking and transformed Burnley's playing style in the process during his first season in charge.
August 11, 2023
Despite the scoreline, the home side were far from outclassed but paid for a slow start and the lack of a clinical finisher like Haaland. Burnley's 2022/23 season finished over a month before City's European Cup final win in Istanbul.
Guardiola has bemoaned his side's short pre-season compared to their rivals, but they were quick out of the blocks. A well-worked corner between De Bruyne, Bernardo Silva and Phil Foden eventually picked out Rodri and his header was fired home by Haaland.
Moments later Burnley were denied a penalty when Manuel Akanji's hold of Zeki Amdouni's arm was not deemed enough for a spot-kick. Luca Koleosho then fired over and Amdouni shot too close to Ederson as Burnley posed a bigger threat for large spells of the first-half.
However, they were hit with a sucker punch when Julian Alvarez laid off Kyle Walker's cross into the path of Haaland to produce an unstoppable effort high past Burnley debutant goalkeeper James Trafford.
With the wind taken from Burnley's sails, City took a stranglehold of the game after the break without ever having to hit top gear. Rodri was the unlikely hero with the only goal in Istanbul two months ago and he started the new season as he finished the last by smashing home from close range after a goalmouth scramble.
Burnley's miserable night was rounded off in stoppage time when Anass Zaroury was shown a straight red card for a wild challenge on Kyle Walker.
August 11, 2023