Curnow slotted six first-half goals and Isaac Heeney kicked five all up as the Swans outclassed the Tigers 25.20 (170) to 8.8 (56) in front of 38,013 fans at the SCG on Saturday.
Despite a raft of injuries, Sydney pulled off the highest-scoring first half of the year, kicking 15.7 (97) to 7.4 (46) at halftime to outdo Adelaide's 14.6 (90) against North Melbourne in round 11.
The Swans condemned the Tigers to their second-biggest loss under coach Adem Yze, whose side suffered a 119-point loss to Brisbane in 2024.
It was the perfect way for the second-placed Swans to return to the winners' circle, after suffering their first defeat in eight games last round to Geelong.
Sydney (10-2) are a chance of returning to the top of the ladder if reigning premiers Brisbane deny leaders Fremantle (10-1) a record-extending 11th straight victory at the Gabba later on Saturday.
The Swans added defender Lewis Melican (hamstring) to their injury list, while hoping Justin McInerney's rolled ankle won't trouble the winger too much.
After their Dreamtime at the 'G victory over Essendon, Richmond fell well short of their first back-to-back wins of the season and remain second-last (2-10).
Curnow reached a new club best, eclipsing his seven-goal haul in their round-seven win over the Western Bulldogs.
The 29-year-old just missed his career-best of 10 goals against West Coast in 2025 when playing for Carlton.
Swans ruck Pete Ladhams (one goal, 28 hitouts) held his ground in the absence of a sore Brodie Grundy, while midfield stars Heeney and Chad Warner fired without injured captain Callum Mills (calf).
Key forward Hayden McLean - in his second match of the season, squeezed out after Curnow's arrival - marked his 100th game with four goals.
Saturday was the first time this season Swans coach Dean Cox played four talls in attack.
"I thought they played well. It's something we've been speaking about for a little bit. Do we go ahead with it? When do we do it?" Cox said.
"To Hayden's credit, he's been in the (AFL) team once and been playing really well for the VFL team and took his opportunity."
Jacob Hopper led Richmond with 25 touches and Jasper Alger slotted three goals, with Sydney simply a class above.
"We got taught a footy lesson today from a really powerful team," Yze said.
"We probably took a couple of steps backwards today.
"It felt like the last month we've been playing the right way.
"Today just wasn't good enough, and when I say it wasn't good enough, it wasn't as good as them."
Richmond started hot, needing less than a minute to nab the opening goal through an unmanned Alger.
Swans tagger James Jordon thundered home from outside the 50-metre arc as a response, before Curnow burst to life to help set up a 20-point lead at quarter-time.
Curnow kicked two goals in the opening two minutes of the second quarter, before coach Yze shifted 20-year-old defender Luke Trainor off the two-time Coleman Medal winner and gave Ben Miller the task.
The Tigers couldn't withstand the onslaught, and Sydney slammed through eight goals to three to take a 51-point buffer into halftime en route to a dominant victory.
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