World No.16 Flavia Pennetta extended her winning streak in the competition to 10 matches with a 6-3, 6-2 triumph over the 31st-ranked Jarmila Groth.
That followed world number four Francesca Schiavone's 7-6 (7/1), 3-6, 7-5 win over fifth-ranked Samantha Stosur in Sunday's first reverse singles rubber.
The wins left the top-seeded Italians with an unassailable 3-1 advantage in the best-of-five match hard-court tie.
Groth registered a fighting 6-7 (4/7), 6-3, 6-3 comeback win over French Open champion Schiavone in her Cup debut for Australia on Saturday, but she was outclassed by Pennetta with the tie on the line.
A WTA title winner in Hobart last month, Groth's service was broken five times in going down in just 65 minutes.
Heading into last year's French Open final rematch with Stosur, Schiavone had spent a total of nine hours, 20 minutes on court in her three previous matches over the past fortnight -- including a record-setting four-hour 44-minute Australian Open win over Svetlana Kuznetsova.
But the redoubtable Schiavone staved off 11 break points and broke Stosur's serve for the only time in the last game of the match to give Italy the winning edge.
Stosur saved three match points in the 10th game of the deciding set and another with an ace in the 12th game before finally succumbing after two hours and 33 minutes.
The final doubles match of the tie was being played Sunday.
Italy cruise to victory over Australia
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