Harry Kane joined Bayern Munich for an initial 100m euros (£86.4m) plus add-ons from Tottenham this summer
Kane swept a low right-footed effort past home goalkeeper Jiri Pavlenka from 15 yards to double Bayern's lead.
He had earlier assisted the first of Leroy Sane's two goals with a deft clip over the top inside four minutes.
Mathys Tel rounded off a comfortable victory for Thomas Tuchel's side late on.
"I was a little bit nervous [and] excited to play the game of course," Kane told broadcaster DAZN after the match.
"We started well with a goal in the first few minutes. For sure there were a few butterflies, but as always when I get on the pitch, instinct takes over."
It was a fine evening for Bayern and the club's record signing Kane, who arrived in Bavaria to great fanfare but had a disappointing start with a 3-0 defeat to RB Leipzig in the German Super Cup.
Billed as the man to finally fill Robert Lewandowski's boots over a year on from the prolific Poland striker's switch to Barcelona, Kane expertly laid on the first goal for Sane.
His quick thinking sent the former Manchester City winger racing clear to roll a low effort into the bottom left corner.
A much-improved Bremen threatened after the break, but Kane dispatched the visitors' second goal of the night, collecting Alphonso Davies' precise pass before picking his spot and placing a low shot into the bottom left corner.
With Kane struggling with cramp, Bayern made several changes.
Substitute Thomas Muller teed up Sane's second goal before Kane's replacement, French teenager Tel, drove in a late fourth.
Bayern have won the previous 11 Bundesliga titles, but their points total of 71 last term, when they only just pipped a faltering Borussia Dortmund, was their lowest since 2010-11 when they finished third.
However, they have sought to remedy that close call with several new signings, including South Korea defender Kim Min-jae from Napoli.
Kane's arrival has undoubtedly caught the imagination the most and provides the greatest cause for optimism they will be able to retain their domestic dominance while challenging again for the Champions League.
Prior to kick-off Tuchel had claimed the "Kane effect" would increase his team's "chances of winning massively" and it is easy to understand why.
While England's all-time top scorer was not at his sharpest, he still provided Bayern with a valuable focal point up front and interchanged superbly with the likes of Sane, Kingsley Coman and Jamal Musiala.
And despite being unable to convert several earlier opportunities to score, in trademark fashion he continued to drop deep, find spaces between defenders and finished unerringly when presented with the ball by Davies.
-- Courtesy of BBC Sport