New Haven, CT, USA, 21 August 2018 | AAP

Sam Stosur has failed to make the most of a lucky loser entry at the Connecticut Open, falling in straight sets to Belarusian Aryna Sabalenka in their first-round encounter.

The world No.25 Sabalenka made short work of the 2011 US Open champion at the WTA event in New Haven, winning 6-3 6-2 in one hour and 11 minutes.

The defeat denied Stosur a second-round meeting against countrywoman and defending champion Daria Gavrilova, who belted Romanian Irina-Camelia Begu 6-2 6-1 a day earlier to advance to the last 16.

Further south in Winston Salem, Australian world No.54 John Millman missed a chance to make the second round in North Carolina.

The 29-year-old Queenslander lost 6-4 7-6(7) to 76th-ranked Japanese Taro Daniel in their first-round match at the ATP 250 event – the final hit-out before next week’s US Open.

Australian 15th seed Alex de Minaur, who had a bye in the opening round, will play Russian Daniil Medvedev on Tuesday.