Moldoveanu held his nerve with a final shot of 10.3 to hold off his rival, who finished just 0.6 behind.
The duo both topped the qualification by equalling the Olympic record and swapped top spots in the final a number of times before Moldoveanu prevailed.
Behind Campriani, Gagan Narang won a bronze medal for India, which was some consolation for the hundreds of Indian supporters crammed into the rifle range after Abhinav Bindra's early exit.
Bindra won India's first individual gold medal at Beijing 2008 four years ago but could only finish 16th in qualifying.
Earlier, Great Britain marksman James Huckle missed out on a place in the final in front of another sell-out crowd at the Royal Artillery Barracks in Woolwich.
He was eventually placed 24th, while the qualification round was won by Campriani, the world number one.
Former Olympic 50m Air Rifle champion Matt Emmons of the USA admitted he is struggling to recapture his form after a score of 590 left him ranked 35th.
'My head's working pretty good but my body's not listening,' he said.
'I'm shooting okay but the scores you need to make the final, around 596, has been around my top hit for a long time.
'It's been coming together over this last month or so but it's still not as consistent as I'd like it to be.'