Having so often been the Australian Open hard-luck stories, Jarmila Gajdosova and Marinko Matosevic both broke long losing streaks at Melbourne Park on Monday.

Gajdosova finally advanced out of the first round of her home grand slam after a decade of trying, beating Alexandra Dulgheru from Romania 6-3 6-4 in 88 minutes.

Matosevic did it tough, coming back from a set down to oust Russian qualifier Alexander Kudryavtsev 6-4 6-7 (5-7) 4-6 7-5 6-3 in a match lasting three hours and 28 minutes.

It was Matosevic’s first singles win at the Australian Open in six attempts and only his third in 18 grand slam matches.

After clinching victory on his second match point, Matosevic fell backwards onto the court in relief and than roared with delight.

Gajdosova faces an extremely difficult second-round encounter against Romanian third seed Simona Halep, who eased past Italy’s Karin Knapp 6-3 6-2 on Monday.

Gajdosova brought some encouraging form into the first grand slam event of the year, having advanced to the quarter-finals of last week’s Sydney International before bowing out in three tights sets to two-time Wimbledon champion Petra Kvitova.

After a difficult couple of years on and off the court, the 27-year-old has got her world ranking back down to 62.

Storm Sanders was the first Australian casualty at the Open, the young wildcard falling 7-5 6-3 to Czech Klara Koukalova.

Wildcard playoff winner Jordan Thompson also fell at the first hurdle, bowing out 6-4 7-6 (7-5) 6-4 to Portugal’s Joao Sousa.

Nine other Australians are in action at Melbourne Park on Monday, including Nick Kyrgios and Bernard Tomic.