Electing to bat, Mike Hussey (50 off 39) and Murali Vijay (35 off 27) shared a 63-run opening stand before skipper Mahendra Singh Dhoni came up with a late 21-ball 31 to guide Chennai to 136 for six in their alloted 20 overs.
Chennai bowlers then rose to the occasion and restricted the Warriors to 126 for eight.
With this victory, Chennai have secured a place in the first semifinal against fellow Indian Premier League side Royal Challengers Bangalore in Durban on Friday.
Even though Warriors lost the match, they too have qualified for the last four stage, pipping Victoria Bushrangers on net run rate.
Chasing the modest 137, Warriors needed 109 to book their their place in the semis and they finally went on to score 126 for eight.
Images: AFP