The race was thrown wide open when it became apparent that defending champion Japhet Kimutai was drifting off the pace.
And Mulaudzi took his chance leading out the pack on the final straight and digging deep to win in a time of one minute 46.32 seconds.
Mutua took silver in 1:46.57, while Australian Kris McCarthy finished the fastest to earn bronze in 1:46.79.
Botswanan Otukile Lekote finished fourth after setting the early pace, while Kimutai was fifth as his bid to become the first 800m runner to defend his title failed.
James McIlroy, of Northern Ireland, came in a respectable sixth.
The South African team had suffered a setback when Hezekiel Sepeng - the Olympic silver medallist - went walkabout and failed to turn up at the Games village.
But Mulaudzi made things better with an excellent gold-medal display.