Once again Jos Buttler 89 off 56 in vain but Royals will have a second shot at the title in Qualifier 2.
Bangladesh were restricted to 365 with Liton Das also scoring a century.
They created history with the win, recording their first series victory over a full-member nation.
Left-arm quick Mustafizur Rahman is in contention to make his return to red-ball.
Liton and Mushfiqur scores twin tons lead Bangladesh fightback after shaky start.
Sunrisers did well to recover from 99 for 6, but their total of 157 was not nearly enough.
Rohit Sharma, Virat Kohli, Jasprit Bumrah among the premier players rested for the series.
India announces squad for fifth test against England, Cheteshwar Pujara returns after successful county stint.
RCB sneak into playoffs after Tim David, Jasprit Bumrah knock Delhi Capitals out.
Rajasthan Royals will face Gujarat Titans in the first Qualifier at the Eden Gardens in Kolkata on May 24.
