Richards was part of Great Britain’s 4x200m relay team that won gold in Tokyo, as was Scott, but this was his first individual Olympic medal.
Richards won the 2023 world title last year but had not hit top form in Paris.
He and Scott were in the 100m freestyle relay quartet that finished fifth on day one and his middling semi-final time left him in an outside lane, where the waves are bigger and quick times rarely swum.
But he overcame that expertly and was in contention throughout.
Popovici, who announced himself in 2022, aged 17, by winning the 100m and 200m gold at the World Championships, looked to be struggling at the start of the fourth and final length but he dug deep, getting the crucial first touch.
“I misjudged the semi-final a bit,” Richards said. “Being out there meant I was a little bit out of the race and I had to swim on my own.
“It is all learning. I want another 10 years before even thinking about hanging the goggles up.”
Scott was bidding for a seventh Olympic medal, another to go with his relay gold and five silvers, but was beaten to bronze by 0.08 seconds.
Such is Britain’s strength in depth in this event, Olympic champion Tom Dean was beaten by Richards and Scott at the trials in April and did not qualify.
The trio will now unite on Tuesday as they bid to defend their relay title, first in the morning heats, although Richards or Scott could be rested before a potential final at 21:01 BST.
Richards also has the 100m freestyle starting on Tuesday, in which he will hope to be among the medals again.
“Myself and Duncan, second and fourth, I am gutted for him, just missing out on a medal,” Richards said.
“It bodes really well for the 4x200m.”