There was a mixed reaction to the controversial scene itself, which lasted for just over a minute and came at the very end of the opera after the music finished.
King Idomeneo arrived on stage with a bloodstained bag containing the four heads and set them out on chairs, Prophet Muhammad last of all.
As he appeared there was one shout of "Stop!" and another audience member then called out "well done!" and there was a smattering of applause.
There followed several calls of "Boo!" answered with shouts of "Bravo!" and then resounding applause for the singers and musicians at the end.
Kirsten Harms, Deutsche Oper's director, said the public's reaction to the scene, designed to symbolise people's release into freedom without gods or idols, was "very civilised".
She said: "This evening art was in the forefront again.
"I hope now that all this media hype will stop."
The opera house's decision in September to cancel Idomeneo caused an outcry among artists and politicians, including Angela Merkel, Germany's chancellor, who said the country should not cave in to the threat of terrorism.
Officials at the production welcomed the change of heart.
Maria Boehmer, a German government representative for foreigners' issues, said: "I am here to send a signal supporting freedom of values and the tolerance of cultures."
Dozens of journalists from around the world were outside the building before the performance, outnumbering the handful of police officers and demonstrators who included Christians and supporters of religious tolerance.
Wolfgang Schaeuble, Germany's interior minister, attended Monday's performance with members of some German Muslim groups, although the central Muslim Council did not attend.
Iman Mazyek, the council's general secretary, said: "It's part of the concept of freedom of opinion and thought that you also have the right to say you are not going."
Mozart's opera tells the story of Idomeneo, a Cretan king, who makes a pact with Poseidon, god of the sea, which leads to him unwittingly promising to sacrifice his son Idamante.
The scene with the severed heads is the invention of Hans Neuenfels, the production's director, and appeared in the show when it was first staged in 2003.
Many of Germany's 3.5 million Muslims say the opera episode has damaged the debate on their integration into society.
As concerns over Muslim militancy have grown in Europe, German Muslims complain of rising Islamophobia, especially since police arrested two Lebanese men suspected of trying to set off bombs on German trains in July.