World number eight Jasmine Paolini then gave Italy an unassailable 2-0 lead with a 4-6 7-6 (7-4) 6-4 win over Wang Xinyu.
Wang also served for the match in the second set but was broken by Paolini – to the disappointment of a boisterous home crowd.
Paolini then came through a tight deciding set to set up a semi-final against either Spain or Ukraine.
“Today was a bit tough for me, but I tried to stay there for the bench, the Italian fans, for the country,” Paolini said.
The doubles match between the two teams was cancelled with the best-of-three tie already decided.
Great Britain, led by Katie Boulter, begin their bid for a first BJK Cup title on Thursday against Japan, with the tie live across the BBC.
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