They could achieve a record-breaking three weightlifting golds at a single Games if favourite Behdad Salimikordasiabi retains his super-heavyweight title on Tuesday.
When Kianoush Rostami broke a world record in winning the 85kg on Friday he predicted more glory to come for Iran.
It arrived in the next event when Moradi won by 8kg, and with two lifts to spare, from Vladzim Sraltsou of Belarus and Aurimas Didzbalis of Lithuania.
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"Now my wish is that Behdad wins his second gold medal, and makes it three for Iran," he said.
Moradi's total of 403kg was 15kg more than his best before a two-year doping ban in 2013.
"During those two years I was on my own at home training very, very hard," he said.
"People laughed at me, they said you're retired, you're banned but I had a goal and I worked hard for it."
Moradi said he did not understand why he was banned and denied having taken any banned substances. He tested positive for methadone and said it must have been administered to him as a painkiller without his knowledge.
Didzbalis, who has also served a two-year ban, might have mounted a stronger challenge but for missing his first two snatch attempts.
He also failed with his final clean and jerk, which he followed with a flying somersault.
"I only do them when I win a medal," he said. "If I had finished fourth you wouldn't have seen it."
The original entry list was shorn of three lifters because of doping.
Two Polish brothers, Adrian and Tomasz Zielinski, were sent home after samples taken before the Games came up positive.
Georgian Rauli Tsirekidze was excluded after testing positive in the reanalysis of samples from the 2008 and 2012 Olympics.
There were two Iranians in the eight-man field and plenty of their countrymen to support them in a crowd of more than 5,000.
Hasem Ali, 24, made only two good lifts for a total of 383kg and seventh place.
Moradi, 27, had two attempts at a world-record clean and jerk of 234kg after his victory was assured, but never came close with either of them because, he said, he felt a strain in his right thigh.
"I am a weightlifter, they are weightlifters, they lost their chance to compete," Moradi said when asked about the bans from these Games of the Zielinski brothers and the 2012 champion Ilya Ilyin, from Kazakhstan.
"I am sad they are not here. I sympathise with them."
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World record and gold for Iran's Rostami