Buchan, driving the sedan version of the i30 run by HMO Customer Racing, was unstoppable in the 14-lap heat to round out the weekend.
He broke from the chasing field, led by race 2 winner Michael Clemente, at the start and was never headed across an affair that ran green until the finish.
Clemente was able to shadow the Hyundai throughout the race but never mounted a serious challenge, the final gap between the pair just under a second.
"We needed that, that was excellent," said Buchan.
"I really wanted [to win] race 3 there. Race 1 was good, pretty comprehensive, as was qualifying. But I wanted to back it up and race 3 and show that it wasn't a one-off.
"There's a long way to go with this car, but we're in the mix."
It was a battle of the Garry Rogers Motorsport Peugeots for third place, with Ben Bargwanna forced to hold off Jordan Cox in the closing stages.
Cox made good progress early in the race to get into fourth but was unable to find a way past Bargwanna.
Bailey Sweeny, in the HMO Hyundai hatch, kept his series lead in tact, capping off a solid if not spectacular weekend with fifth in race 3.
His margin now sits at 22 points over Cox.
Aaron Cameron ended up sixth from two drivers running the latest-spec Audi, Zac Soutar (Team Soutar Motorsport) and Will Brown (Melbourne Performance Centre).
Tom Oliphant capped off Lynk & Co's Australian debut with a ninth in race 3 ahead of Lachlan Mineef (Forza Brakes Motorsport Audi) and reigning champion Tony D'Alberto (Wall Racing Honda), who struggled to recover from a costly tyre failure yesterday.
The 2023 TCR Australia season continues at Winton on June 9-11.
