Bayern Munich were not the biggest club in their own city, let alone the country, when Gerd Muller signed in 1964.

The Bavarians' major trophy haul at that time consisted of a single league championship in 1932 and a maiden DFB-Pokal success 25 years later. Muller joined a second-tier side.

On Tuesday, two days after the club great's passing, Bayern celebrated his life in fitting fashion with a record-extending ninth DFL-Supercup triumph – a competition they have to win silverware simply to enter.

The Bundesliga dominance, cup after cup and six European crowns... all that history can be traced back to Muller's decision to head for Bayern rather than rivals 1860 Munich.

He was there for the first four Bundesliga titles – the top scorer on each occasion – and for three European Cups in three years, Muller's standards slipping as Jupp Heynckes was the leading marksman in the third season.

In 15 years, the remarkable forward tallied 566 Bayern goals, a benchmark that stands to this day. Muller's Bundesliga total of 365 is also unsurpassed.

As those numbers show, breaking a Muller record is no simple task, but Robert Lewandowski finally did so last season when scoring 41 goals in a single Bundesliga campaign, edging beyond the legend's 40 in 1971-72.

"I achieved a goal that once seemed impossible to imagine," Lewandowski wrote on his Twitter page in May. "I'm so unbelievably proud to make history for Bayern, and to play a part in creating the stories that fans will tell their children – following in the footsteps of legends like Gerd Muller."

It made sense then for Lewandowski to be front and centre again at Signal Iduna Park as Muller was remembered.

He clutched a number nine shirt ahead of kick-off as a moment's silence broke into applause, the Borussia Dortmund fans recognising a legacy that goes beyond club lines.

It was a lovely tribute, but Muller would have been more familiar with Lewandowski's subsequent nods to his greatest predecessor.

Muller was the ultimate 18-yard box centre-forward, a mantle Lewandowski has taken on and exhibited expertly against his former side.

Manuel Neuer, another of the Bayern players carrying a Muller shirt, kept Dortmund at bay at one end – finishing with four saves – before his club's latest outstanding number nine showed Erling Haaland and BVB's team of young pretenders how it is done at the other.

"Lewandowski has proven over several years now that he is a world-class striker," coach Julian Nagelsmann said before the game. "Erling hasn't been in the league that long, although his scoring rate is great."

That proven Lewandowski class brought a brutal, brilliant opener, his header from Serge Gnabry's left-wing cross thumped into the bottom-left corner. The outcome of a chance that was worth a moderate 0.29 expected goals (xG) was never in doubt.

And Lewandowski was involved again, in the box again, when Bayern appeared to put the game beyond doubt four minutes after half-time, waving a leg towards Alphonso Davies' low cross in an attempt at a flick that ran instead for Thomas Muller's tap-in, the late Bayern superstar's namesake having been the third visiting player to hold up a red shirt in a pre-match show of respect.

Perhaps the linesman was a Gerd Muller fan, too, twice ruling in Bayern's favour when Youssoufa Moukoko and Haaland each ran away to score – the second call considerably closer than the first.

There was no ruling out a blistering Marco Reus strike, which briefly threatened Bayern's control, but Manuel Akanji's dallying let Lewandowski in again and the Dortmund fans know exactly how that tends to go. This time with an xG of 0.25 – merely the fifth-best chance of the match – the 32-year-old made it look routine.

A seventh Supercup strike, Lewandowski extended another record that is all his own – albeit in a competition Muller never graced.

The Poland international is Muller's nearest challenger in Bundesliga terms, with 278 goals, and deserves to be counted in such company, even if he has just added to Bayern's reputation rather than transformed it. Lewandowski has also now scored in 14 successive matches for Bayern, which means he needs to score in just two more consecutive games to match another of Muller's all-time records (16, in 1969-70).

Meanwhile, this was not Haaland's night, but he too could have one eye on the sort of standards Muller set. Still just 21, Haaland has 42 goals in 44 Bundesliga games – or one every 84.8 minutes – and Hasan Salihamidzic has acknowledged Bayern would be "amateurs" not to consider signing the striker.

Given the apparent inevitability of a transfer at the end of this campaign, the BVB sensation would seemingly have to join Germany's powerhouse to stay in the Bundesliga and close on Muller or Lewandowski.

Bayern do not need a replacement up front just yet, though, after their latest legend ensured 2021-22 would continue an almost constant theme since Muller broke all barriers, with silverware heading back to Bavaria.