With main rivals VfL Wolfsburg and Gladbach playing Sunday, Pep Guardiola’s Bayern claimed their eighth win in 11 league games to pull clear of the chasing pack against Thomas Schaaf’s Eintracht.
“Once we get into our stride, we’re difficult to stop,” said Bayern’s Germany defender Jerome Boateng, who set a new Bundesliga record of 50 games unbeaten in matches in which he has played.
Having been rested for Wednesday’s 2-0 home win over Roma, which confirmed Bayern’s place in the Champions League last 16 as group winners, Mueller opened the scoring from a Franck Ribery pass at the second attempt on 23 minutes.
The 25-year-old then boosted his tally with two goals in three minutes after converting another Ribery pass after the Frenchman sprinted through the defence with Poland striker Robert Lewandowski also queueing up to score on 64 minutes.
Mueller bagged his third to leave him with nine goals in all competitions and the league’s joint top scorer when he finished off a move from a quick Ribery throw-in to claim his sixth Bundesliga goal.
Xherdan Shaqiri grabbed the fourth on 86 minutes after fellow second-half replacement Arjen Robben had pulled the Frankfurt defence to pieces to leave the Swiss winger to tap into an empty net.
“It’s always hard to play against a team from Thomas Schaaf,” said Guardiola.
“They were very aggressive in defence, we had a few problems with our structure, but the last 20 minutes was a completely different game.”
Werder Bremen can move off the bottom, and leave last season’s runners-up Borussia Dortmund last before hosting third-placed Borussia Moenchengladbach on Sunday, with just a point at VfB Stuttgart on Saturday evening.
Hoffenheim dropped to fifth after a lively 4-3 defeat at home to Cologne with Nigeria striker Anthony Ujah netting his third goal of the season for the visitors and Poland defender Pawel Olkowski scoring twice, including the 83rd-minute winner.
Leverkusen, who won 2-1 at Zenit St Petersburg on Tuesday to stay top of their Champions League group, were held to a goalless draw at home to Mainz and drop to sixth having suffered a shock 1-0 league defeat at Hamburg last weekend.
Robert di Matteo suffered his second consecutive defeat as Schalke coach when his side lost 2-0 at Freiburg, who pulled clear of the relegation places to move up to 13th with Christian Guenter and Jonathan Schmid scoring their goals.
The 44-year-old Di Matteo has now lost three and won three of his six games since taking charge last month and his side drop to 11th in the table — exactly where they were when he took charge.
Augsburg moved up to seventh with a 3-0 win at mid-table Paderborn as midfielder Tobias Werner scoring twice.
Second-placed Wolfsburg can pick up their eighth straight win when they host strugglers Hamburg on Sunday.
Hanover 96 moved up to fourth in the table with a 2-0 win at Hertha Berlin on Friday.