The Italian team will hope the celebrations continue at Suzuka in two weeks after Albert Park breathed new life into the championship.
Sainz and teammate Charles Leclerc's 1-2 in Australia trimmed Red Bull's lead to four points in both the drivers' and constructors' title races, a major momentum shift following Max Verstappen's Middle East dominance.
Ferrari had the fortune of Verstappen flaming out with a brake problem at Albert Park which ended Red Bull's two-year run of avoiding DNFs (non-finishes) on race-day.
Ferrari nonetheless leave Melbourne delighted by the pace of their SF-24 car after being trounced by Red Bull in Saudi Arabia and Bahrain.
"This weekend is good evidence that when we are putting everything together, and I’m not sure that we’ll be able to do it every single weekend, but we can put (Red Bull) a little bit under pressure,” said team boss Frederic Vasseur.
"It's when they are under pressure that they will also have more mistakes. We have to continue in this direction."
With triple world champion Verstappen topping the podium ahead of teammate Sergio Perez in the season's first two races, Red Bull were blindsided by setup struggles from the get-go in Melbourne.
Red Bull team boss Christian Horner said Red Bull had not got to grips with conditions while Ferrari clearly, had.
"I think the nature of the surface (was a factor), as well. I think that the tyre graining here in particular was something that Ferrari looked in control of," he said. "Certainly from Friday their long runs looked good."
Perez, who finished fifth after the floor of his car suffered damage, said Ferrari "absolutely" had the pace to beat Verstappen had the Dutchman gone the distance. However, Red Bull advisor Helmut Marko was unconvinced.
"I spoke to Max and he said that, despite the problems, he kept up with Sainz's pace relatively easily," Marko told Sky Sport. "With Max in the race, it would have turned out completely differently."
Ferrari may not know where they sit until their next proper duel against Verstappen, who won 19 out of 22 races last season and will be eager to hit back at the Japanese Grand Prix. Mercedes, by contrast, can have little doubt of their place in the pecking order, with Melbourne confirming their also-ran status.
With no championship points at Albert Park and their first double DNF since 2018, the Silver Arrows have slumped to fourth in the championship, 71 points behind leading Red Bull.
The free-fall may continue as the Brackley-based team battle to understand the fluky performance of their overhauled W15 car.
"We haven't swallowed a dumb pill since 2021. It's just we don't understand some of the behaviours of the car," said team boss Toto Wolff.
