Australia's Nick Kyrgios overcame an early injury scare to win his first-round match at the US Open against Briton Aljaz Bedene on day two at Flushing Meadows.

In the end, Kyrgios completed a 6-4, 6-4, 6-4 victory in one hour 57 minutes on the Old Grandstand court.

Kyrgios started well early, and he won the first set in 37 minutes. But towards the end of that set he appeared to struggle with his mobility, and he could be heard on a changeover telling a trainer he had a hip problem which was getting worse.

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On completion of the set he had a medical timeout, before coming back to resume the match.

The Australian seemed to get some of his mobility back as the match went on, attempting an athletic jump volley at 4-2 in the second set.

The 14th-seed Kyrgios had too much in reserve for the Briton, who is ranked 77th in the world.

Aside from the injury, Kyrgios had the latest in a string of on-court issues.

He received an unsportsmanlike conduct penalty in the opening game, for hitting a ball to close to a line judge after a ball was called out.

He remained frustrated for the rest of the match, and avoided shaking the chair umpire's hand immediately after closing out the third set.

Kyrgios will now face Horacio Zeballos in the next round after the Argentinian defeated Germany's Florian Mayer in straight sets.

Stosur through, Gavrilova out

Samantha Stosur will face China's Zhang Shuai after her first-round win over Italy's Camila Giorgi. ( Getty Images: Elsa )

Earlier, Australia's Samantha Stosur advanced to the second round with a solid three-set win over Italy's Camila Giorgi.

The 2011 champion started well but was pegged back before dominating the latter stages of the match to clinch a 7-5, 6-7 (7/4), 6-1 win.

The first set was a tight affair, as both players struggled to hold serve - there were five service breaks in all, the last of them coming with a forehand winner from Stosur to clinch the opener in 52 minutes.

The Italian broke Stosur to lead 4-2 in the second set, only for the Australian to hit back and lead 5-4 to be only one game from victory.

The set went to a tie-break, with Stosur throwing in a double fault for 2-3. She got the break back with a forehand winner for 3-4, but Giorgi pulled out a backhand winner to gain the advantage and she won the set with an ace.

If there were any nerves from Stosur at the change in the match, they didn't show, as the Australian charged out to a 4-0 lead in the deciding set before completing the win in two hours 37 minutes.

Stosur will now play Zhang Shuai for a place in the round of 32, after the Chinese player defeated another Australian, Ellen Perez, 6-1, 6-1.

Daria Gavrilova bowed out of the women's singles with a straight sets, 6-4, 6-4 loss to Czech player Lucie Safarova.

Gavrilova was under pressure from the start, broken in the opening game of the match. Safarova held her serve throughout to take the set in 37 minutes.

The Australian held serve to start the second set, but was broken as Safarova led 2-1, and then another break for 5-2 looked to have sealed the win for the Czech.

Gavrilova rallied with a break back, and held her serve for 5-4, but Safarova forced an error on the Australian's forehand to complete the victory in one hour 28 minutes.

Safarova will now play fifth seed Simona Halep of Romania in the second round.

Tomic beaten by Dzumhur

Bernard Tomic bowed out of the US Open in controversial fashion, losing to Bosnia-Herzegovina's Damir Dzumhur in four sets.

Tomic, the men's 17th seed, won the third set after going 2-0 down, but he lost 6-4, 6-3, 4-6, 7-6 (7/0) in two hours 38 minutes.

However the disappointing result was overshadowed by a foul-mouthed spray Tomic aimed at a spectator during the match.