Needing 140 runs to win, Chennai chased down the target with five balls to spare.
Du Plesis kept on playing sensibly throughout when no other batman clicked and went back cheaply. He played 42 balls and slammed five boundaries and four sixes.
Hyderabad will now face the winner of the match between Kolkata Knight Riders and Rajasthan Royals in Qualifier 2 on May 25 at Kolkata.
Brief scores: Sunrisers Hyderabad: 139/7 in 20 overs (Carlos Brathwaite 43 not out; Dwayne Bravo 2/25) against Chennai Super Kings: 140/8 in 19.1 overs (Du Plesis 67; Rashid Khan 2/12)