Radwanska looked to have regained control when she led 4-0 in the third set but only sealed the win by reeling off the last two games when Jankovic drew level at 4-4.
Jankovic actually won two more points than Radwanksa overall but still finished behind in their floodlit thriller.
"I should have finished it a little bit earlier in the third set, but she was really fighting until the last point," Radwanksa said.
"I think I was just better in a couple of points today. I'm happy I could win this one."
Halep only needed an hour to wrap up a lopsided victory and is poised to become the first Romanian woman to break into the top five when the updated world rankings are released on Monday.
The only other Romanian woman to make the top 10 were Virginia Ruzici, who won the French Open in 1978 and made it up to number eight in the world, and Irina Spirlea, who climbed as high as seven.
"It means a lot," Halep said. "I'm now the best Romanian in history for rankings - but my goal is to win a Grand Slam, and then maybe I'll be the best, because Virginia won the French Open."
BNP Paribas Open results
2-Agnieszka Radwanska (Poland) beat 7-Jelena Jankovic (Serbia) 7-5 2-6 6-4
6-Simona Halep (Romania) beat Casey Dellacqua (Australia) 6-2 6-2
- Sports & Recreation
- Simona Halep