The Bavarians struck three times in the 30 minute first-half.
Thiago grabbed his first for the club after Franck Ribery and Phillip Lahm had given Pep Guardiola’s side a two goal advantage.
Toni Kroos had already fired over when Ribery angled Arjen’s Robben’s cross home with a controlled volley to open the scoring with 17 minutes gone.
Ribery turned provider when the Bavarians doubled their advantage five minutes later as he won the ball in midfield and drove to the by-line before cutting back for Mueller, who saw his shot blocked.
Lahm, who was playing in midfield, followed up to double his side’s lead.
Thiago's resourcefulness brought Bayern a third with 26 minutes gone as he chested Jerome Boateng’s cross home from close range to put the game beyond Lucien Favre's men.
De Jong gave the home faithful something to cheer on the stroke of half-time when he coolly slotted home a penalty after Diego Contento’s over-zealous challenge had felled Patrick Herrmann inside the box.
Robben put paid to any hope of Monchengladbach comeback in the second-half when he headed a Ribery cross home to re-open a three goal advantage ten minutes in.
Mueller finished off the scoring with 60 minutes on the clock with a simple tap-in after good work from Ribery.
In the third place play-off Jonas Hoffmann got the only goal as Borussia Dortmund beat Hamburg 1-0.
Cristiano Ronaldo scored twice as a star-studded Real Madrid side gave Championship side Bournemouth a tough lesson with a 6-0 romp at Dean Court.
Sammy Khedira, Gonzalo Higuain, Angel di Maria and Casemiro also scored as Real showed little mercy in front of a capacity crowd.
Galatasaray scored a last-minute equaliser after having a man sent off in a 3-3 draw with Bernd Schuster’s Malaga.
Wesley Sneijder finished off a quick break with a dipping, swerving effort from outside the box to open the scoring with 12 minutes gone.
Roque Santa Cruz restored parity on the stroke of half-time with a composed finish but Didier Drogba gave the home side the advantage at the break with a trademark header deep into first-half injury time.
Bobley Anderson headed the visitors back level with 57 gone before Dany Nounkeu received a straight red card having conceded a penalty.
Duda retained his composure to give his side the lead from the spot with 74 minutes on the clock before Kazim Kazim-Richards grabbed the leveller in injury time.
Getafe had two players sent off as AZ Alkmaar beat them 3-0 in a pre-season friendly.
The hosts were two goals to the good inside the opening quarter of an hour through strikes from Roy Beerens and Viktor Elm.
Getafe regrouped but the game was over as a contest when Michel saw red for a second bookable offence in the 58th minute.
Aron Johannsson grabbed a third for AZ with 78 gone before Pablo Sarabia received a straight red with six minutes remaining.
Julian Draxler was on the scoresheet as Schalke 04 played out a 1-1 draw against Besiktas.
Borussia Dortmund target Draxler struck from distance in the 58th minute to open the scoring before Franco grabbed a leveller eight minutes later to ensure a share of the spoils.
Bordeaux came from a goal down to secure a 2-1 against KV Mechelen.
KV Mechelen took a lead to the interval courtesy of a 35th minute Thomas Enevoldsen penalty but strikes from Ludovic Obraniak in the 59th and Cheick Diabeté in the 76th ensured the win for Francis Gillot’s men.
Nathan Dyer and Rory Donnelly got the only goals as Swansea City won 2-0 at Exeter.