Sam Billings is out, Shane Watson is in for Chennai Super Kings. He played 42 balls and slammed five boundaries and four sixes.
The Kane Williamson-led Hyderabad, who topped the league table, have a second chance of making the final in the second qualifying match Friday when they will meet the victor of an eliminator.
Chasing 140 to reach the final for the seventh time, Chennai were gasping at 62 for six when South African Du Plessis mounted a spectacular counter-attack to see them home with five balls to spare at Mumbai's Wankhede Stadium.
Yusuf Pathan contributed 24 but it was Carlos Brathwaite's 43 not out from 29 balls that helped Hyderabad post 139-7, however it was not enough in the end.
CSK skipper Mahendra Singh Dhoni, too, didn't last long.
The umpire Marais Erasmus signalled it a dead ball as Dhoni collected the delivery, which was surprising as the batsman expected it to be called a no-ball, which would give his team a run and a free hit.
Former Black Caps captain Stephen Fleming now works as a T20 coach, with the Chennai Super Kings in the IPL and for the Melbourne Stars in Australia's Big Bash League. It's not easy when you don't play a lot of games but I always say you need to train your mind as well.
While captain Dhoni had missed an earlier opportunity for a run out from point-blank range, Chennai were otherwise ruthless and Dwayne Bravo (2-25) provided the standout wicket.
Wary of the dew factor later in the evening, Dhoni had earlier opted to field against 2016 champions Hyderabad and paceman Deepak Chahar gave Chennai a flawless start by dismissing opener Shikhar Dhawan for a first ball duck.
Sunrisers' bowling this season have been extraordinary with Rashid and Shakib as well as the pace trio of Bhuvneshwar, Siddarth Kaul and Sandeep Sharma, combining well to defend paltry totals.
Earlier, Hyderabad top order stuttered against seamers in the batting powerplay as Shikhar Dhawan dragged Chahar back onto his stumps off the first ball. Sunrisers captain Kane Williamson has led from the front; he's not only been prolific with the bat but has also been smart with his captaincy. Brathwaite was particularly harsh on Thakur, scoring 20 runs off him in the last over of their innings.
"The game did swing our way, and bowlers were outstanding, but we didn't quite execute it like in the past", Williamson said. "Faf played a lovely knock, and credit to the way they scrapped it".