Venus Williams (R) shakes hands with Johanna Konta
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Williams, who had lost her last three encounters with the British number one, showed no signs of nerves as she dictated play from the baseline and broke Konta twice in the first set.
Konta recovered to take the second set and level the match but Williams, who won the Rome title in 1999, came back spectacularly with a decisive double break in the third set.
The American will meet either defending champion Garbine Muguruza, a 7-5 6-4 victor over Julia Goerges, in the quarter-finals.
Garbine Muguruza of Spain in action
Estonian qualifier Anett Kontaveit, who defeated world number one Angelique Kerber on Wednesday, continued to build momentum with a 6-1 6-1 victory over 16th-seed Croatian Mirjana Lucic-Baroni.
Sixth-seed Simona Halep marched past Russia's Anastasia Pavlyuchenkova 6-1 4-6 6-0 in the other third-round clash. The Romanian will face Kontaveit in the quarter-finals.
Unseeded Daria Gavrilova stunned Russia's Svetlana Kuznetsova to reach the final eight of the competition with a 2-6 7-5 6-4 victory.
Sir Chris Hoy & Joanna Rowsell