The Francisco Roig era of Emma Raducanu’s career began with a positive performance as the 30th seed defeated Olga Danilovic of Serbia 6-3, 6-2 on a sweltering day in the second round at the Cincinnati Open.

Raducanu’s recent progress has been driven by her reliability against inferior opponents and she is now 19-4 against lower-ranked players over the past year. Having spent much of the past four years struggling to string together wins, she is now as match-tough as she has ever been.

A far greater test awaits Raducanu, who had received a first-round bye owing to her status as a seeded player, in round three. A Wimbledon rematch is guaranteed as she will either face the world No 1, Aryna Sabalenka, her conqueror in the third round, or the 2023 Wimbledon champion Marketa Vondrousova, who Raducanu defeated in round two this summer.

During her one previous appearance in Cincinnati two years ago, where she dismantled Serena Williams in the final month of her career and Victoria Azarenka in consecutive matches, Raducanu showed that the faster courts here suit her well. This time, however, she had the oppressive heat to deal with. The temperature on Champions Court rose to 30C (85F) with considerable humidity.

Raducanu opened the match poorly with three loose unforced errors and a double fault to drop her opening service game to love. Constant aggression from Danilovic, an ultra-offensive lefty with a big serve and forehand but poor movement, allowed the Serb to dictate the majority of the early exchanges. In the opening games, Raducanu was forced to scrap behind the baseline, chasing down balls while trying to elicit unforced errors from her opponent for much of the first set.

Francisco Roig has been brought in as Emma Raducanu’s new coach. Photograph: Frey/TPN/Getty Images

However, Raducanu’s depth of service return was brilliant from the beginning, consistently refusing Danilovic the short balls she was looking for behind her first serve. Raducanu also defended well, maintaining her depth and patiently looking for opportunities to take the ball early and attack. In the face of this intensity, Danilovic’s error count rose throughout.

After struggling on serve early on, Raducanu gradually grew in confidence. From her uncertain position behind the baseline, she ended a composed, efficient performance striking the ball early and putting Danilovic’s laboured movement under constant pressure as she eased into the third round.

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One year after missing most of the North American swing, including the Cincinnati Open, before her first round loss at Flushing Meadows, Raducanu is in quite a different position. Her run on the hard courts began with two positive showings, reaching the semi-finals of the WTA 500 event in Washington before winning two matches last week in Montreal. Now she will have another opportunity to test her level against one of the world’s best.