Mary Kom, a Khel Ratna awardee and nicknamed 'Magnificent Mary' for her unprecedented five world titles, out-slugged Chieh Meng Ping of Chinese Taipei 16-2.
She will face China's Cancan Ren, who defeated Nepal's Sanju Lama 10-0.
Kavita (75kg), however, had to put up with stiff resistance from Marina Volnova of Kazakhstan before coming out trumps 8-7.
However, it was heartbreak for Preeti Beniwal (60kg) who had to concede her bout against Thai Tassamalee Thongjan after twisting her knee midway through the third round.
Beniwal was trailing 0-3 when an attempted attack on Thongjan went horribly wrong and she fell awkwardly to pick up the injury.
Mary Kom was in destructive form on Monday against a hapless rival who was scurrying for cover as the Indian rained blows.
With a combination of left hooks and right jabs, Mary Kom dominated from the beginning and it was not until the third round that Ping got on the scoring sheet.
The two points that Ping managed were courtesy a defensive lapse by the Manipuri mother-of-two, who kept her guard perilously low all through the bout.
Kavita's bout was, however, a tense affair and she was locked 5-5 with her rival after three rounds. It was in the final two minutes that the Indian managed to edge past the Kazakh.