The Spanish international striker signed for Chelsea from Real Madrid in a deal reported to be worth up to 80 million euros ($92m) last week, and climbed off the bench with about 30 minutes remaining of the match.
But German international Mueller, whose future has been rumoured to be in doubt after Bayern's loan signing of James Rodriguez, was the outstanding player in a competitive pre- season friendly.
Playing in front of a crowd of over 48,000, it took Bundesliga champions Bayern just six minutes to score with Brazilian defender Rafinha rattling a 25-yard drive past Chelsea goalkeeper Thibaut Courtois, who should have done better.
This time the on-form winger Franck Ribery picked out the unmarked Mueller with a deft chipped cross, and the forward volleyed home in acrobatic fashion.
Also Read
With Chelsea struggling to find their rhythm and all at sea at the back, a moment of brilliance from Mueller saw the Germans extend their lead, as he curled a shot past Courtois after surging through the centre for 3-0.
Chelsea's response came in first-half stoppage time as a Victor Moses cross found Marcos Alonso, and the defender drilled past Bayern goalkeeper Tom Starke.
Morata made his mark on the game 13 minutes later, flicking on a corner for Michy Batshuayi to finish.
The game was part of the International Champions Cup, which brings together top-tier teams from Europe.
Disclaimer: No Business Standard Journalist was involved in creation of this content