The Pole was beaten 6-7(2) 6-1 6-2 in exactly two hours by her Romanian opponent, who had lost in all their previous three meetings.
Halep was superior in all areas as she recorded a second upset in Italy after disposing of Svetlana Kuznetsova in round one.
After a close first set, Radwanska was resoundingly beaten in the next two. Halep will face either 13th seed Roberta Vinci or Nastassja Burnett in the last 16.
Radwanska won WTA tournaments in Auckland and Sydney early this year but has not claimed one since.
Bojana Jovanovski upset 10th seed Caroline Wozniacki 2-6 6-4 7-6(5) in almost three hours in their first-round match.
Two breaks of serve allowed Wozniacki to wrap up the first set 6-2 in just under 40 minutes.
The Dane was favourite having recorded a 6-4 6-4 win against Jovanovski in Madrid in 2011 before claiming a 6-0 3-6 6-4 victory over her last season in Tokyo.
But the former world number one is horribly out of form having lost in the opening rounds of the Madrid Masters and Stuttgart Open, and world number 44 Jovanovski took the second set 6-4 despite a leg injury.
Wozniacki really should have wrapped up the deciding set, having led 4-1 and then 5-2 in the tie-breaker but her worrying run of form continues with Jovanovski securing a first win since January.
Eighth seed Petra Kvitova lost a bagelled second set against Sabine Lisicki but won the other two to move into round three.
WTA Rome results
1-Serena Williams (U.S.) beat Laura Robson (Britain) 6-2 6-2
Simona Halep (Romania) beat 4-Agnieszka Radwanska (Poland) 6-7(2) 6-1 6-2
8-Petra Kvitova (Czech Republic) beat Sabine Lisicki (Germany) 6-4 0-6 7-5
Carla Suarez Navarro (Spain) beat 11-Nadia Petrova (Russia) 3-6 6-2 7-6(1)
Romina Oprandi (Switzerland) beat Anastasia Pavlyuchenkova (Russia) 6-2 6-0
16-Sloane Stephens (U.S.) beat Flavia Pennetta (Italy) 6-3 6-3
Urszula Radwanska (Poland) beat 15-Ana Ivanovic (Serbia) 6-3 2-6 6-2
Yanina Wickmayer (Belgium) beat Kirsten Flipkens (Belgium) 6-4 6-0
Zheng Jie (China) beat Magdalena Rybarikova (Slovakia) 7-6(0) 6-3
13-Roberta Vinci (Italy) beat Elena Vesnina (Russia) 6-7(2) 7-5 6-4
14-Dominika Cibulkova (Slovakia) beat Kristina Mladenovic (France) 1-6 6-2 6-2
Bojana Jovanovski (Serbia) beat 10-Caroline Wozniacki (Denmark) 2-6 6-4 7-6(5)
Julia Goerges (Germany) beat Andrea Hlavackova (Czech Republic) 2-6 6-4 6-4
Varvara Lepchenko (U.S.) beat Lesia Tsurenko (Ukraine) 6-4 6-2
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