Middleweight Marshman, the first Welshman to appear on a main UFC card, beat Canadian Ryan Janes on points.
Johns got the best of American Albert Morales in their bantamweight fight on the preliminary card.
Johns' bout in March was cancelled after his opponent pulled out, while Marshman lost his last fight to Thiago Santos in Canada.
Marshman, the Abertillery paratrooper who has toured Afghanistan twice, beat Sweden's Magnus Cedenblad on his debut in Belfast last November.
Johns, from Pontarddulais near Swansea, also won that night and described those results as "absolutely ginormous" for the sport in Wales.
Johns's original opponent for UFC Glasgow, Mitch Gagnon, pulled out two weeks ago, but Morales stepped in to ensure he will have his second UFC bout.
Marshman had originally signed to fight fellow Welshman John Phillips in Glasgow, but injury forced the Swansea fighter to pull out.
"I signed the contract, he signed the contract. The fight was on," Marshman said.
"But he fell out injured apparently. It is what it is. I'm not chasing him
Welsh mixed martial arts fighters Jack Marshman and Brett Johns earned their first UFC wins of 2017 in Glasgow.