The 29-year-old five-time world champion fought her way to a 15-6 victory and there was no disguising her delight.
She said: 'I'm so, so happy. This is the first time women's boxing has been included in the Olympics. I waited for so many years to be a part of the Olympics and when I have become a part of it, it feels so good to go back home with a medal.'
Kom, weighing 46kg, is fighting in a higher category than she is used to, with Fly Weight allowing boxers to weigh up to 51kg.
She said: 'If there was a lower weight category that was included in the Olympics, I would have definitely been an Olympic champion.
This is a new weight category for me and I am just glad that everything's working for me. I have been trying to gain weight so badly. All I do is eat, eat and eat.Mary Kom
'But this is a new weight category for me and I am just glad that everything's working for me. I have been trying to gain weight so badly. All I do is eat, eat and eat.'
Kom, who will face Britain's Nicola Adams next on Wednesday, had the lead from the opening round against Rahali as she manoeuvred her way around her opponent, winning the approval of the crowd.
The Indian said: 'I feel so good when I hear the crowd shouting out my name. They say 'Go Mary!' and that actually makes me step up my game.'
China's world champion Ren Cancan also proceeded to the semis after defeating Russian Elena Savelyeva 12-7.
American Claressa Shields was off to a slow start as she lost her first two rounds to Swedish Anna Laurell in the Middle Weight quarter-finals. But Shields fought back to clinch a semi-final berth.