Bayern produced a football master class in the UEFA Champions League Group E clash at the Stadio Olimpico, with a five-goal haul practically wrapping up the points before half-time.
Arjen Robben scored twice either side of goals from Mario Gotze and Robert Lewandowski, before Thomas Muller made it 5-0 with a contentious penalty.
Roma peppered the Bayern goal at the start of the second half and Manuel Neuer - who was chasing a ninth competitive clean sheet in a row - was finally beaten when Gervinho headed home in the 66th minute.
It proved a mere blip for the visitors, though, as Franck Ribery scored a sublime chip and fellow substitute Xherdan Shaqiri rounded off the scoring in the closing stages.
Despite the apparent gulf in class, Bayern coach Guardiola believes Roma will show they are a force to be reckoned with in the return match at the Allianz Arena on November 5.
"We found an early goal with Arjen and that calmed us," he told Sky Sport Italia. "Then we pressed Roma to keep hold of the ball. We do it because we want the ball, not to irritate our opponents.
"We like to hold the ball and then probe to find where we can break through. We will see in two weeks in Munich that there is not such a huge gap between the teams.
"In 20 minutes Roma had three or four clear scoring opportunities and therefore we have to improve, so we'll talk things over."
Bayern can confirm their progress to the knockout stages by beating Roma in Munich as Manchester City could only draw 2-2 at CSKA Moscow in the group's other encounter on Tuesday.
Guardiola is keen for his side to remain focused and see out the task in hand.
He added: "Manchester City drew their game in Moscow, so Roma remain second, it's still only in October."
