A feisty Novak Djokovic moved into the quarter-finals of the Internazionali d'Italia by seeing off Roberto Bautista Agut in straight sets on Thursday.
Del Potro enjoyed success on the Djokovic serve in the first game of the match, but did not win another game in the opening set as the Serbian ruthlessly seized control.
The Serb clinched the match at the fourth time of asking after Bedene sailed a forehand long after an hour and 46 minutes on court.
Isner, ranked 24th in the world, reached the last-eight on Thursday when he upset world number three Stan Wawrinka of Switzerland 7-6 (7/1), 6-4. "I'm going out there against the No. 3 player in the world. The last time we played I won in Paris a year ago, the indoor tournament in Paris", added Isner. Maybe I have a little bit less to lose than he does.
On the other hand, Del Potro, who skipped the early-season action in Australia, stunned seventh seed Kei Nishikori 7-6 (4), 6-3 to claim a win against a top-10 opponent for the first time since his victory over Tomas Berdych at 2012 French Open. That's what happened today.
Meanwhile, unseeded American John Isner battled into the Rome Masters semis with a 7-6 (7/3), 2-6, 7-6 (7/2) win over Croatian sixth seed Marin Cilic.More news: Pennsylvania man jailed; 3 kids found alone, toddler caged
Zverev, the 16th seed who is the youngest player in the ATP top 50, will meet the victor of the clash between Tomas Berdych and Milos Raonic, to be played later Thursday.
In the women's draw, Venus Williams defeated Johanna Konta 6-1, 3-6, 6-1. "It's one of my favorite places on earth, so that's one of the reasons why I have always come here".
Second-seeded Karolina Pliskova is also safely through after easing past experienced clay-court player Timea Bacsinszky 6-1, 7-5.
Djokovic recently broke off his association with his coaching staff, playing in Madrid accompanied on the bench by his brother, Marko, and he said on Monday that he has not yet decided who will be his next coach.
"I'm just really trying to take it match by match and setting these really small goals", the 21-year-old Kontaveit said.
Halep surged into the last-four for the third time after a 6-2, 6-4 win over Estonian qualifier Anett Kontaveit.