Kane set up Olise for the opening goal in the 23rd minute, and then showcased his skills by dribbling down the right and delivering a pinpoint pass for Jamal Musiala to score soon after.
Olise then assisted Kane's 57th-minute goal, the England captain's 10th goal so far for Bayern this season in six games all competitions.
Olise scored again and Kane set up Serge Gnabry to make it five against Bremen, whose only win against Bayern dating back to 2008 came this January in Munich.
Kane scored his first Bundesliga goal on debut at Bremen in August last year and now has 41 league strikes, more than any other English player.
"We've got so much quality up front and we're having fun playing football," Musiala told Sky, adding "but we will face tougher opponents."
Bayern host champions Bayer Leverkusen next Saturday.
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Fellow top-four rivals Leverkusen, Borussia Dortmund, Stuttgart and RB Leipzig all play on Sunday, but Bayern are guaranteed to finish the weekend in top spot as the only side to have won all four of their opening league matches.
Two goals in the opening six minutes put Union Berlin on course for a 2-1 win at home against Hoffenheim.
Tom Rothe and Jeong Woo-yeong scored early for the home side but a 67th-minute goal from former Union forward Marius Buelter set things up for a nervy finish in the German capital.
Union however dug deep to win their second match of the season and keep their unbeaten record alive, while Hoffenheim have lost their past three in the league.
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Freiburg scored three second-half goals to win 3-0 at Heidenheim, with Italy midfielder Vincenzo Grifo getting a double after Ritsu Doan opened the scoring.
An 89th-minute goal from Shuto Machino snared a 2-2 draw for Holstein Kiel at Bochum, giving the promoted side their first-ever points in the top division.
Kiel took the lead through a Benedikt Pichler goal after 15 minutes but Matus Bero and Lukas Daschner both scored to give Bochum a 2-1 advantage at halftime.
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Later on Saturday, Eintracht Frankfurt host Borussia Moenchengladbach.
(Except for the headline, this story has not been edited by staff and is published from a syndicated feed.)