Jack Graham kicked two crucial final-quarter goals as the Tigers posted a 12.16 (88) to 11.9 (75) victory at the MCG on Thursday night to move within touching distance of the top eight.
But debutant Jacob Bauer limped off with a hamstring injury in the opening two minutes and there was another sour note when Nankervis caught Swans defender Jake Lloyd with a high bump.
Lloyd was substituted out with concussion during the second quarter after an incident that will attract scrutiny from the league's match review officer.
Replays showed Nankervis' shoulder making contact with Lloyd's head, leaving Swans coach John Longmire seething.
Nankervis (18 disposals, six clearances, 32 hit-outs) went on to be one of Richmond's most influential players as the home side enjoyed a 47-31 clearance differential and overwhelmed their opponents after half-time.
"He had a big role and unfortunately Jakey Lloyd didn't have any role in the game, which was disappointing," Longmire said.
"But he got on top in the ruck and really gave them momentum out of there."
Richmond stars Dustin Martin (29 disposals, six clearances) and Dion Prestia (22, six) were outstanding on return alongside Shai Bolton (31, nine) and Tim Taranto (29, nine).
Graham and substitute Jack Ross kicked two goals apiece, while young defender Tylar Young had some big moments opposed to Sydney superstar Lance Franklin.
Richmond trailed by as much as 26 points during the second quarter but dominated the second half and kicked four goals to one in the final term.
The result hung in the balance until Graham and Martin popped up with goals deep into time-on of the last quarter.
It means the Tigers could end the round just two points outside the top eight.
"We've had some challenges late in games over the past couple of years so we've put a fair bit of work into that space," interim coach Andrew McQualter said.
"Ultimately it's about leaders and people standing up in the final moments and our guys were really able to do that tonight.
"The beauty of a win like that, particularly in the second half, was we had a lot of contributors."
Franklin kicked two goals on return from injury in what was likely his final appearance at the MCG, with retirement looming at the end of the season.
But the 36-year-old champion squandered the chance to put his side back in front with a missed set shot during the final term.
Isaac Heeney (three), Justin McInerney and Will Hayward (two each) also kicked multiple goals for Sydney.
Errol Gulden (31 disposals), Oliver Florent (30) and Luke Parker (28) were busy for the Swans, who were left to rue a second-half fade-out in a loss that leaves them battling to stay in finals contention.
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