Australian wildcard Kimberly Birrell has stunned world number 29 Donna Vekic to reach the third round of the Australian Open.

Key points: Kimberly Birrell was granted a wildcard entry to the Australian Open, with her ranking certain to skyrocket after win over 29th seed

Kimberly Birrell was granted a wildcard entry to the Australian Open, with her ranking certain to skyrocket after win over 29th seed Alex De Minaur triumphed in five sets to set up clash with Rafael Nadal, who beat Matthew Ebden in straight sets

Alex De Minaur triumphed in five sets to set up clash with Rafael Nadal, who beat Matthew Ebden in straight sets John Millman fell short after a tremendous comeback, losing in five sets to Roberto Bautista Agut

The shock result came on a mostly positive evening for Australian players, with Alex De Minaur also advancing to the third round, though there was an epic loss for John Millman while Matthew Ebden lost to Rafael Nadal.

Ranked 240 in the world — though that is now sure to rocket upwards — Birrell held her nerve to see out a 6-4, 4-6, 6-1 win over the Croatian to set up a potential clash with second seed Angelique Kerber, who beat Brazilian qualifier Beatriz Haddad Maia 6-2, 6-3.

"It is so surreal. That was just such a blur but all I know is I left it all out there," Birrell said.

"I used the energy from the crowd and they were the best. I get to play again. It's crazy."

The elegant Birrell was out-aced 12-7 by her more-esteemed opponent, but enjoyed a far-more accurate serve, delivering fewer double faults and hitting fewer unforced errors, while dominating at the net.

A string of winners in the deciding set saw the German-born Gold Coast native streak clear to clinch the match, before soaking up a huge applause on Court Three.

"There were so many things going through my head," she said.

"I had to bring myself back to the present and focus on getting my first serve in."

Birrell has made the most of her wildcard entry to the Australian Open, having beaten Spanish qualifier Paula Badosa Gibert in the first round in straight sets.

Kimberly Birrell is an accomplished baseline player, but won vital points at the net to progress to the third round. ( AAP: David Crosling )

Progression to the last 32 will precipitate a rankings rise for the 20-year-old, with a cheque of at least $165,000 awaiting her.

That windfall could be even higher should she produce the shock of all shocks in beating Kerber, a former winner in Melbourne and a three-time major singles champion.

Birrell was born to Australian parents in Dusseldorf, Germany, while her father John was working as a tennis coach.

She moved to Australia at the age of three when John took up a posting as the head coach at Pat Cash's Tennis Academy on the Gold Coast.

A baseline player who favours the hardcourt, Birrell has two ITF titles to her name, and made a splash earlier this year with a win over world number 10 Daria Kasatkina of Russia at the Brisbane International, before losing in the round of 16.

The Demon accounts for Swiss challenger

Alex de Minaur plays a backhand return against Henri Laaksonen. ( AAP: Julian Smith )

Australia's leading male player De Minaur lived up to his burgeoning reputation despite a hiccup or two along the way with a gruelling five-set win over Switzerland's Henri Laaksonen.

De Minaur, 19, powered through the first two sets before working up a sweat in a tie-break loss, before Laaksonen fought back to win the fourth set and level the match up.

But De Minaur broke at the crucial time to triumph in the final set, setting up a tantalising clash with second seed Nadal.

Rafael Nadal did not have too much trouble against Matt Ebden on centre court. ( AP: Mark Schiefelbein )

Nadal accounted for another Australian as he saw off the challenge of Matt Ebden, winning in straight sets.

The Spaniard proved far too canny for Ebden, winning 6-3, 6-2, 6-2 on Rod Laver Arena.

Epic comeback halted as Millman falls short

Birrell's compatriot John Millman almost conjured up a Lazarus-like comeback, but ran out of puff at the death in a five-set thriller against Roberto Bautista Agut.

John Millman nearly pulled his match from out of the fire, but came up short in the final set. ( AP: Kin Cheung )

Spain's Bautista Agut, the 22nd seed who vanquished Andy Murray in the opening round, shook off a two-set comeback from Millman to ultimately win 6-3, 6-1, 3-6, 6-7, 6-4.

Down two sets, Millman roared back to take the third set 6-3.

But looking worse for wear in the fourth-set tie breaker with the match on the line, Millman summoned up tremendous courage to spark a comeback.

Down 6-2, Millman saved four match points, winning six consecutive points in total to take out the tie-break 8-6 and level the match.

That resurgence looked to have taken its toll, however, as Millman saw his serve broken before Bautista took a 4-2 lead in the final set.

More frustrations erupted as Millman showed visible anger at a lost point on his service, shaking his racquet furiously as he netted a forehand.

Millman regained his composure, winning the game on his serve, but it proved too little, too late as Bautista Agut served out the match.