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 Could, rallied to interrupt and draw stage at 4-4.
Having compelled Kostyuk to serve to remain within the match, the Ukrainian double faulted handy Raducanu two match factors, which the Briton took on her second probability.
The 2021 US Open champion stated it was an “extraordinarily good win”.
“I am pleased with the way in which I fought via the primary set and within the second, stayed robust 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 remaining 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 enjoying “like a child once more”, Norrie stated: “I simply sort of let go of the expectations and I am enjoying tennis extra to take pleasure in it now.
“You have to take pleasure in it in any other case you may get burned out on this lengthy schedule.”
