Held to one handball in the first quarter and three marks in the first half, Franklin lifted in the final term to finish with four goals, including the last of the match as the Swans held off the Tigers by 11 points.
Richmond defender Alex Rance earned Longmire's praise his job on Franklin, but it was the Swans' superstar who eventually shaped the result by converting the few chances he was given.
"We kicked nine and he's kicked four straight in a low-scoring game … he kicked some crunch goals at important times," Longmire said post-match.
"I thought Rance did a pretty good job at times as well, but to be able to kick four goals at clutch times was important.
"Clearly he's able to do thing at different times that you need an experienced player to do and he did some really good things tonight."
Friday night's win was a typically blue-collar effort from the Swans, who recovered from a poor start that saw them concede six of the first eight goals and fall 26 points behind in the second quarter.
Longmire said it "wasn't a great game of footy" but the Swans were able to will themselves over the line without playing well.
He said last week's testing clash against ladder leader Port Adelaide couldn't be blamed for the side's slow start.
"Regardless of what happened last week, we didn't bring our best in the first 10 minutes," he said.
"In the end we found a way. We've played four of the other top five sides over the last eight or nine weeks and we've been pretty competitive and having a real crack.
"Fortunately we were able to turn that around and we had some really strong efforts from our leaders and a few of the young kids."
Longmire reserved praise for debutant Zak Jones, who started as the substitute and showed composure when injected into the game in the second half.
He replaced injured defender Rhyce Shaw, who rolled an ankle and will require scans. Kieren Jack also appeared to suffer a wrist injury, but Longmire said he had been cleared of damage.
