Williams, who served five aces in one game, looks unstoppable but issued a few words of caution.
"Nothing is ever perfect - I learned that last year when I felt perfect," Williams said, referring to her first-round loss at last year's French Open. "I am still in the danger zone.
"I can't remember the other winning streaks, but I hope I can get to 22 and the rest of the matches that I have here.
"Plus seven, and Wimbledon too, so it would be dangerous to lose now."
Williams was joined in the quarter-finals by Maria Sharapova who breezed past Sloane Stephens 6-2 6-1 while Serbia's Jelena Jankovic, a former Rome champion showing signs of a return to her best form, beat China's fifth seed Li Na 7-6 7-5.
Rome Masters (women) round three results:
9-Samantha Stosur (Australia) beat 8-Petra Kvitova (Czech Republic) 7-5 2-6 6-1
2-Maria Sharapova (Russia) beat 16-Sloane Stephens (U.S.) 6-2 6-1
3-Victoria Azarenka (Belarus) beat Ayumi Morita (Japan) 6-1 2-0 (Morita retired)
1-Serena Williams (U.S.) beat 14-Dominika Cibulkova (Slovakia) 6-0 6-1
Simona Halep (Romania) beat 13-Roberta Vinci (Italy) 6-4 6-2
Carla Suarez Navarro (Spain) beat Lourdes Dominguez Lino (Spain) 6-2 6-3
7-Sara Errani (Italy) beat 12-Maria Kirilenko (Russia) 6-3 2-0 (Kirilenko retired)
Jelena Jankovic (Serbia) beat 5-Li Na (China) 7-6(2) 7-5
- Sports & Recreation
- Maria Sharapova
- Jelena Jankovic