Dane Sweeny, Tristan Schoolkate, Chris O'Connell and Bernard Tomic were the victors, the first three of those living up to being seeded 11, 28 and 32 respectively.
However, James McCabe and Alex Bolt are out.
Tomic now plays O'Connell with the winner one match away from a place in the main draw.
Tomic, a Wimbledon quarter-finalist 15 years ago aged 18, defeated Japan's Kaichi Uchida 6-3 6-2. O'Connell, fresh from winning his first grass-court event, the Nottingham Open, on Saturday, beat Joel Schwaerzler of Austria 7-6 (7-3) 6-4.
Schoolkate defeated local wildcard Johannus Monday 7-5 6-3 and will next meet another Briton, Dan Evans. The 36-year-old former world No.21 is trying to reach his final Wimbledon the hard way after criticising the organisers' decision not to hand him a wildcard. He has announced he will retire after the championships.
Sweeny, like Schoolkate bidding to reach his first Wimbledon, eased past Franco Roncadelli of Uruguay 6-4 6-2 and now meets American Darwin Blanch.
McCabe lost to former Wimbledon quarter-finalist Roman Safiullin. After a one-sided first set he put up more of a fight before succumbing 6-1 7-6 (7-4).
Bolt went down 7-6 (7-3) 7-5 to Britain's Oliver Tarvet.
Emerson Jones, Taylah Preston, Storm Hunter and Maddison Inglis begin their qualifying campaigns on Tuesday, also hoping to join the dozen Aussies who have already booked a place via their ranking.
There were similarly mixed fortunes for Australians in the Wimbledon warm-ups, inevitably so to at the Mallorca Open where wildcard Nick Kyrgios faced qualifier Adam Walton.
The younger man broke in the eighth game, going on to take the first set 6-3. Despite Kyrgios showing flashes of his brilliance at the net Walton then snatched a crucial break in the ninth to take the second set 6-4.
On England's south coast at Eastbourne Alexei Popyrin suffered a surprise defeat to British qualifier Jan Choinski 1-6 6-2 6-2. Aleksandar Vukic plays Tuesday.
In the women's event Maya Joint had expected to meet Swiss veteran Viktorija Golubic but instead found herself facing lucky loser Emiliana Arango. After a tight first set she lost 7-6 (7-2) 6-4 to the Colombian.
Daria Kasatkina also lost, 6-3 7-6 (7-3) to American McCartney Kessler. But there was an impressive victory for Ajla Tomljanovic who beat Italian eighth-seed Elisabetta Cocciaretto 6-2 6-7 (5-7) 7-5.
Most of the attention at Devonshire Park was on British former world No.4 Jack Draper who was making his comeback after an injury-plagued year with two-time Wimbledon winner Andy Murray debuting in his coaching box.
Draper beat American lucky loser Marcos Giron 6-4 7-6 (7-5) and said: "I suppose today was a performance a bit like what he used to: winning ugly."
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