After Wednesday's order of play was washed out by rain, the British number one sprung a surprise on seventh seed Sloane Stephens on Thursday morning in a second-round encounter, coming through 6-7(3), 6-4, 6-1.
That secured her a fourth consecutive round-of-16 spot in Rome, and a clash with veteran Venus, who won the tournament in 1999.
The seven-time Grand Slam champion had a 4-3 advantage in their head-to-head record - and had also got the edge in Rome, beating the Brit at the same stage two years ago.
But Konta came out firing, hitting 36 winners after breaking the Williams serve in the very first game.
Konta had already beaten Stephens' and Williams' compatriot Alison Riske 6-4, 6-1 in the first round.
She now faces either Daria Kasatkina or Marketa Vondrousova in the final eight.