Erling Haaland scored twice before Rodri completed the scoring to give City a perfect start to their quest to become the first side to win four consecutive English top-flight titles.
But the night was soured for Pep Guardiola’s men by the sight of De Bruyne limping off midway through the first-half.
The Belgian had suffered a hamstring tear in City’s Champions League final victory over Inter Milan two months ago.
“He was injured again unfortunately,” said Guardiola. “Same place and position as the Champions League and he will be out for a while.
“It depends on the magnitude but will be a few weeks out. He has to free (his) mind and relax because he came back from that position (previous injuries) and he will be back now.”
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.
“We are still not in our best (physical) form but we have to try to not drop many points in that period,” added Guardiola. “It’s a question of mentality and we were fortunate to break the game early.
“A lot of teams are going to suffer here, so that is why I am so pleased.”
Haaland fired City to the treble 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 after a well-worked corner between De Bruyne, Bernardo Silva and Phil Foden.
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.
Despite the scoreline, the home side were far from outclassed but paid for the lack of a clinical finisher like Haaland.
Luca Koleosho and Zeki Amdouni missed good chances to equalise, while Amdouni also had a penalty appeal turned down.
“There were a lot of periods of the game where we did ourselves proud,” said Kompany.
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 in off the underside of the bar nine minutes before half-time.
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 Walker.
Kane on brink of Bayern move
Meanwhile, England captain Harry Kane arrived in Germany yesterday after Tottenham manager Ange Postecoglou confirmed the striker is on the brink of signing for Bayern Munich.
The two clubs have reportedly agreed a fee worth an initial £86 million (B3.8 billion) for the 30-year-old, who had just one year left on his contract at Spurs.
Kane was given permission to travel to Germany to complete a medical ahead of what would be a record transfer for a Bundesliga club.
He arrived in the early evening for his exam in central Munich, an AFP photographer said.
Postecoglou is preparing to take charge of his first game in charge of Tottenham at Brentford tomorrow and said he is now planning on life without the club’s all-time top goalscorer.
“My understanding is it has progressed to the point where it looks like it will happen,” said Postecoglou at his pre-match press conference.
“From that perspective at least it gives us some clarity and we move forward without Harry.
“From my perspective it is just about understanding where we are at and the information I have at the moment is the deal is imminent, but like with all these things, you leave yourself some leeway.
“But moving forward and training today preparing for Brentford, we are doing it without Harry.”
‘No agreement’
Earlier yesterday, Bayern boss Thomas Tuchel said the six-time European champions were working on the deal as their “highest priority”.
Tuchel’s men kick off their season against RB Leipzig in the German Super Cup today with the start of the Bundesliga season not till next weekend.
“We are working hard on it... that is no secret,” said the former Chelsea manager.
“But as of now there is no decision. As long as there is no agreement, the coach is not going to talk about it, as it is not his player.”
Kane scored 280 goals in 435 games for Spurs and is also England’s all-time top goalscorer with 58 international goals.
However, he is yet to win a major trophy at club or international level.
Silverware is all but guaranteed at Bayern, who have won 11 straight Bundesliga titles.
But the German giants were in desperate need of a striker after struggling to replace Robert Lewandowski last season. Lewandowski moved to Barcelona at the end of the 2021-22 campaign.
The club won the Bundesliga in each of the Pole’s eight seasons in Munich, with Lewandowski scoring 344 goals in 375 appearances.
The Polish international averaged 30 goals per season. In 2022-23, not one Bayern player hit the 15 league goal mark.
Kane has scored more than 20 league goals in all but three of the past nine Premier League seasons, winning the golden boot on three occasions.
Despite finishing second in last season’s Premier League scoring charts behind Erling Haaland (36), Kane netted 30 league goals in 2022-23, equalling his best mark.
Bayern were eliminated by eventual winners Manchester City in the quarter-finals of the Champions League last season and only won the Bundesliga title on goal difference thanks to a final-day capitulation from Borussia Dortmund.