Pep Guardiola’s second-placed Bayern are now level on points and goal difference with leaders Borussia Dortmund after Saturday’s impressive 4-0 win in Gelsenkirchen.
“We’re improving from game to game and we will get better from week to week,” said centre-back Boateng whose Bayern side host Hanover 96 in the second round of the German Cup on Wednesday.
It was Schalke’s worst home league defeat since May, 1981.
Guardiola, who took charge of the European champions in June, hailed Bayern’s display.
“That was our best performance so far in the Bundesliga, we dominated against one of the best teams in Germany,” said Guardiola after his side enjoyed 70 percent ball possession against Schalke.
Despite a bright opening 20 minutes, Jens Keller’s Schalke undid their good work with two defensive lapses in the space of three minutes.
First Bastian Schweinsteiger, then striker Mario Mandzukic were left unmarked in the area to head home for Munich.
Schweinsteiger, back in the starting side after straining ankle ligaments last month, smashed home Arjen Robben’s corner on 21 minutes and just 99 seconds later, Mandzukic converted David Alaba’s cross.
France winger Franck Ribery and then replacement striker Claudio Pizarro added late goals as Schalke’s four-match winning run came to an abrupt halt.
Bayern have now gone 31 games without losing a Bundesliga match and have recorded 26 league wins and five draws since losing 2-1 loss to Leverkusen in October 2012.
Having won their first five league games, league leaders Dortmund could only manage a 1-1 draw in Nuremburg.
Left-back Marcel Schmelzer’s first-half free-kick was cancelled out by Nuremberg centre-back Per Nilsson’s second-half strike.
Dortmund coach Jurgen Klopp brought a weakened team to the Grundig Stadium with centre-back Mats Hummels missing with a back injury.
Star striker Robert Lewandowski and midfielder Henrikh Mkhitaryan started on the bench and were rested after Dortmund’s 2-1 Champions League defeat at Napoli on Wednesday.
Both Schmelzer and attacking midfielder Marco Reus are doubtful for Tuesday’s German Cup second-round match at second division 1860 Munich after picking up leg injuries.
Bayer Leverkusen remain third after their 4-1 win at Mainz 05, which featured two first-half goals from Australian striker Robbie Kruse – his first Bundesliga goals for Leverkusen since joining from Fortuna Düsseldorf.
The 24-year-old tucked home a through ball from Germany winger Sidney Sam after 19 minutes, set up Sven Bender for Leverkusen’s second, then converted a pass from captain Simon Rolfes for Bayer’s third just before half-time.
The league’s joint top-scorer Stefan Kießling then scored his fifth goal of the season when he headed home unmarked early in the second half. Mainz midfielder Yunus Malli grabbed a late consolation for the home side.
Hanover 96 stay fourth after a 2-1 win at home to Ausgburg with Hungary midfielder Szabolcs Huszti netting an 89th-minute penalty.
After sacking coach Thorsten Fink last week in the wake of their 6-2 drubbing at Dortmund, Hamburg slumped to their fourth defeat of the season, losing 2-0 at home to neighbours Werder Bremen.
Wolfsburg moved up to sixth with a 2-1 win at home to Hoffenheim as Croatia’s ex-Bayern striker Ivica Olic scored both goals for the Wolves.
On Sunday, VfB Stuttgart drew 1-1 with Eintracht Frankfurt, a result which left both teams in mid-table. Stuttgart striker Vedad Ibisevic missed two clear chances including a 93rd-minute penalty.
After successive defeats, Hertha Berlin picked up their first point in three games with a 1-1 draw at Freiburg.
Striker Admir Mehmedi’s early goal for Freiburg was cancelled out by Norway international midfielder Per Skjelbred’s first-half equaliser.
Despite the point, Freiburg remain second from bottom after three draws and three defeats, while Berlin are tenth.