The Caribbean star anchored the Dhaka innings with a blazing knock before picking up three wickets on Tuesday to help his team secure a berth in the title-decider.
Khulna will now face Rajshahi Kings, who beat Chittagong Vikings in the eliminator earlier in the day, to reach the final.
Riding on a late resistance led by Russell's gritty 46, Dhaka posted a modest 140-8 at the Sher-e-Bangla National Cricket Stadium in Mirpur.