Kane, who arrived in Germany on Saturday after a mega-money move from Premier League side Tottenham, assisted on Leroy Sane's opener just three minutes in, before scoring midway through the second half.
Billed as the missing link one year after the German champions lost forward Robert Lewandowski, Kane connected play superbly on his Bundesliga debut, going close several times before his 75th-minute opener.
Kane's goal snuffed out Bremen's second-half fightback and opened the floodgates.
Sane scoring another and French teenager Mathys Tel, who had replaced Kane, getting on the scoresheet in injury time to ensure Bayern finished the opening day in their usual place: atop the league table.
"It was a good night" Kane told broadcaster DAZN after the match. "We started well with a goal in the first few minutes."
"I was a little bit nervous (and) excited to play the game of course.
"For sure there were a few butterflies, but as always when I get on the pitch, instinct takes over."
Kane's opposing number nine, Germany striker Niclas Fuellkrug said his side's poor first half forced them to take risks in the second.
"Against Bayern it's always risky, they have quality and they have speed."
Winners of the past 11 straight Bundesliga titles, Bayern last lost a season opener in 2011, They had not lost in the first round as defending champions since 2001.
After hobbling to last season's title, Bayern came into the season under scrutiny, particularly after they were whacked 3-0 by RB Leipzig in last Saturday's German FA Supercup.
Kane settled Bayern's nerves early, setting up Sane's goal after just three minutes.
Collecting a close-range Sane pass on the halfway line after just three minutes, Kane chipped the ball over the Bremen defence and back to the former Man City winger.
Sane, often criticised for wasting chances since arriving back in Germany, ran 30 metres before gliding the ball past goalie Jiri Pavlenka and into the bottom corner.
Missing injured newcomer Naby Keita, a surprising summer addition from Liverpool, Bremen fought back through last season's top scorer Fuellkrug.
The Germany striker had the ball in the back of the net after eight minutes, but his headed effort was struck off for a narrow offside.
Bremen fended off Bayern for the remainder of the opening stanza and started the second half strongly, before Kane controlled a pass from Canada defender Alphonso Davies and shot. The ball took a slight deflection on its way into the back of the net.
Kane was subbed off with five minutes remaining to be replaced by Tel who scored in injury time to seal a comfortable win for the visitors.
