The nail-biting quarterfinals finished 2-2 in the stipulated 90-minute at the Bangabandhu National Stadium.
Saif Sporting frustrated the 10th champions Mohammedan with a 7-6 win in the sudden-death tiebreaker.
They will play their fellow port city team Chittagong Abahani in the first semifinals on January 6 at 4pm at the same venue.
The day’s crucial match saw three goals scored within the first 11 minutes when Saif SC was leading by 2-1.
Later, Souleymane of Mohammedan neutralised the match in the dying moments of the first half.
Atikuzzaman put The Black and Whites ahead in the second minute of the game while Emmanuel of Saif SC scored an equaliser in the seventh minute.
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Next, Ikechikeu put Saif SC ahead, scoring the second goal for the side in the eleventh minute.
Souleymane levelled the match in the 44th minute, leading the match towards the tiebreaking session as both the teams failed to produce any goal in the extra time.
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Both the teams spoiled one chance each in the first five attempts of the tiebreaker.
And in the sudden-death session, Mohammedan scored two goals from three attempts. But Saif SC did not make any mistake and won the match 7-6, converting the last three attempts successfully.
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Sheikh Jamal DC will take on Bashundhara Kings in the third quarterfinals on Sunday while Dhaka Abahani will play Uttar Baridhara in the fourth quarterfinals on Monday at 4pm.