The 43-year-old French driver was followed by fellow RML driver Tom Chilton in second place, with Alex MacDowall third.
Behind the three, Gabriele Tarquini and Tiago Monterio gave the new Castrol Honda WTCC team plenty to cheer about by bringing their two Civic cars home in fourth and fifth places respectively.
"It was very hard because the rain was getting harder and harder every lap," Muller told Eurosport after the race.
"I lost my wiper in the second lap and Tom was giving me a bit of pressure, so I am pleased.
"In these conditions you can't go 100 per cent. It is easy to make mistakes so I went at 99 percent.
"I hope my mechanics will fix my wiper for Race 2, but the story is different when you start from the pack and it will be tricky in those conditions. I will do my best and my aim is to score points; the Championship is a long one!"