Chasing 181, SRH rode on a brilliant knock from Ishan Kishan, who smashed 70 off 47 balls with three fours and seven sixes. Heinrich Klaasen also played a key hand with 47 as SRH chased down the target in 19 overs.
With the victory, SRH became the third team after Royal Challengers Bengaluru and Gujarat Titans to qualify for the playoffs. Hyderabad now occupy third place in the points table with 16 points from 13 matches and an improved net run rate of +0.350.
Earlier, CSK posted 180/7 after contributions from Dewald Brevis (44) and Kartik Sharma (32). SRH skipper Pat Cummins starred with the ball, picking up 3/28 in his four overs.
Despite the defeat, CSK remain sixth in the standings with 12 points from 13 games. However, their net run rate slipped to -0.016, further hurting their playoff hopes heading into the final league game.
Punjab Kings continue to hold fourth place with 13 points from 13 matches, while Rajasthan Royals are fifth with 12 points from 12 games and a slightly better NRR than CSK.
Delhi Capitals are seventh with 12 points from 13 matches, while Kolkata Knight Riders remain eighth with 11 points from 12 matches.
At the bottom, Mumbai Indians and Lucknow Super Giants have already been eliminated from playoff contention with eight points each.