Spaniard Alonso will start fourth on the grid at Albert Park, with Max Verstappen on pole and Mercedes drivers George Russell and Lewis Hamilton second and third respectively.
Alonso was second on the grid in Jeddah after Ferrari's Charles Leclerc was handed a penalty, but he said Aston Martin had closed the gap with Red Bull in Australia.
"In terms of performance, arguably, this was the best qualifying for us of the three (races)," Alonso told media.
"It's the closest we've been to pole position, so I feel fast and the car is easy to drive and I enjoy it."
Alonso's fastest lap in qualifying was just over four-tenths of a second shy of Verstappen's, a slight improvement on his gap with Red Bull pole-sitter Sergio Perez in Jeddah.
Alonso, who came third in both of the first two races of the season and grabbed his 100th podium in Jeddah, said that it would be hard to get ahead of the Mercedes cars on Sunday but that Aston Martin's strength was on the long runs.
"I feel confident, I feel positive about tomorrow," said the Spaniard, whose team mate Lance Stroll qualified sixth.
"Our strength is, I think, the long run pace so we start in the first two rows of the grid and our strengths are on Sundays -- let’s use it," he said.
Aston Martin and Mercedes are equal second in the constructors' championship on 38 points, well behind Red Bull on 87.
