Sun will remain in Melbourne for the women’s doubles, partnered with Hungary’s Fanny Stollar.
However, the Kiwi faces a tall order, up against the tournament’s top seeds – Katerina Siniakova of the Czech Republic and Taylor Townsend of the USA – in the first round on Wednesday.
Despite the significant gulf in world ranking places in her favour, Sun couldn’t assert herself in the opening set of her losing singles effort.
As the early exchanges went with serve, Kovinic broke Sun to take a 4-2 lead, and held to leave the Kiwi serving to stay in the first set.
And although Sun was able to hold, Kovinic doing the same at the other end gave the Montenegrin the opening set in just half an hour, taking it 6-3.
With her back against the wall, Sun was broken again at the start of the second set, despite saving four break points in doing so, to fall 2-1 behind in the opening stages.
However, starting to find the form that saw a run to the Wimbledon quarter-finals in 2024, Sun immediately broke back to square the ledger and then survive break point at the other end for a 3-2 advantage.
Two games later, though, Sun missed three attempts at breaking Kovinic to go 5-3 ahead in the second, and as both players held serve, a tiebreak loomed.
But when Sun couldn’t hold at 5-5, Kovinic had the chance to serve for the match. In no time, Kovinic raced to 40-0 up for three match points and needed only one to end the Kiwi’s tournament 6-4, 7-5.
Alex Powell is an Online Sports Editor for the NZ Herald. He has been a sports journalist since 2016, and previously worked for both Newshub and 1News.