Radwanska had beaten Jankovic in their last four meetings, but this one was as close as it could be - after closing out a marathon 56-minute first set, 7-5, Radwanska watched on as Jankovic started to find the range on her huge down-the-lines, ripping them for winners and cruising in the second set, 6-2.
The third was incredibly streaky - first Radwanska went up 4-0, then Jankovic caught up to 4-all, even holding a break point for 5-4. But instead it was the No.2-seeded Radwanska who won that game and then broke one last time to get past the No.7-seeded Jankovic in two hours and 33 minutes, 75 26 64.
The match was so tight that Jankovic actually won two more points than Radwanska - 105 to 103.
"First of all, it was a very good match from the beginning 'til the end," Radwanska said. "For sure I should have finished it a little bit earlier in the third set, but she was really fighting until the last point. I think I was just better in a couple of points at the end today. I'm really happy I could win this one."
Radwanska is through to the semifinals of the BNP Paribas Open for the second time in her career, having gone this far in 2011 before falling to Caroline Wozniacki (who lost to Jankovic in the final).
Radwanska leads Halep in their head-to-head, 3-2, though Halep has won their last two meetings.
"Simona's having a really unbelievable season, and last year as well," Radwanska said of the soon-to-be-World No.5. "I lost to her just a few weeks ago in Doha - I didn't play badly in that match, but she was just playing some unbelievable tennis. I couldn't do anything to win that match against her.
"I'm really looking forward to it, especially now that she's going to be in the Top 5 as well."