Boulter, who had gone into qualifying in Melbourne off the back of winning the ITF W60 Canberra final, was pushed to a deciding-set super tiebreak by Caroline Dolehide, which she edged for a 6-2, 3-6, 7-6 win.
Jodie Burrage, whom Boulter had beaten in that Canberra final at the weekend, was also victorious with a relatively straightforward 6-2, 6-4 win against Australia’s Elysia Bolton.
Burrage, though, struggled with her first serve, with just 47 per cent of them landing in across the two sets.
There were a trio of wins in all from the British women on Tuesday as Yuriko Miyazaki held off the challenge of Hailey Baptiste 6-4, 7-5, Miyazaki the more clinical in converting four of six break points in contrast to the American’s two from seven.
Strong start: Britain’s Katie Boulter beat Caroline Dolehide in Australian Open qualifying on Tuesday
/ Getty ImagesAnd Katie Swan, who had impressed during the United Cup for Great Britain, last week was the only British woman to bow out in qualifying during the day, losing 6-4, 6-3 to Frenchwoman Jessika Ponchet.
The hopes of the British men in qualifying, however, ended on Tuesday. Ryan Peniston, who had shone in the grasscourt warm-up events to Wimbledon last year, was defeated in straight sets by Canada’s Alexis Galarneau.
And then Liam Broady agonisingly missed out to Emilio Gomez 6-3, 6-7, 7-6, Broady losing the super tiebreak to the No4 seed 10-7.