Raducanu, the British quantity three, took the opening set after a gruelling 71 minutes, regardless of sacrificing a 4-0 lead within the tie-break.
She then held a 3-0 benefit within the second set however Kostyuk, who had misplaced 5 singles matches in a row since Might, rallied to interrupt and draw stage at 4-4.
Having pressured Kostyuk to serve to remain within the match, the Ukrainian double faulted handy Raducanu two match factors, which the Briton took on her second likelihood.
The 2021 US Open champion mentioned it was an “extraordinarily good win”.
“I am pleased with the best way I fought by means of the primary set and within the second, stayed powerful once I wanted to,” she added.
Norrie, in the meantime, managed solely three winners within the first set, two of them on aces, however dominated the second to pressure a decider.
After saving 5 break factors within the fifth recreation of the ultimate set, he broke Musetti, who had a first-round bye, within the sixth to take a 4-2 lead.
The Italian saved two match factors within the closing recreation – one on a Norrie double fault – however then despatched a backhand past the baseline, handing the Briton victory after two hours and 7 minutes.
Admitting he was taking part in “like a child once more”, Norrie mentioned: “I simply form of let go of the expectations and I am taking part in tennis extra to get pleasure from it now.
“You have to get pleasure from it in any other case you may get burned out on this lengthy schedule.”
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