The event is being played alongside the WTA Finals, featuring the world's top eight singles players and eight double pairs in Singapore.
Karman will now meet Taipei's Hsiang-Wen Huang, who beat Japan's Eri Shimuzu 7-5 2-6 10-3 in the other semi-final.
At the Kallang Tennis Centre on Friday, Karman withstood a late revival to see off Khafiany, 6-1 7-5, while Huang overcame a mid-match wobble to defeat Shimuzu, 7-5 2-6 10-3.
Interestingly, Karman beat Hsiang in the league stages.
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The Indian won each of her matches in straight sets.
In the U-14 event, India's Mahak Jain crashed out in the semi-finals. Yuki Ando proved far too strong for Mahak winning 6-3 6-1. Ando will meet Thasaporn Naklo for the title.
The other semifinal proved a far closer affair, with Naklo fighting back to get past Ni Ma Zhouma, 6-7(5) 6-4, 6-2.
Mahak won four of her five league matches to qualify for the semi-finals.
The winners will be presented with the trophy by two-time Grand Slam champion Li Na. The BNP Paribas WTA Finals presented by SC Global begins next week.