Klaasen scored an unbeaten 59 from 41 balls as the Titans recovered from 102-6 to post 151-6. He was well supported by fast bowler Junior Dala, who made 27* off 18.
The Titans lost Quinton de Kock (five) and captain Theunis de Bruyn (nought) early on.
Eighteen-year-old debutant Dewald Brevis – who was bought by the Mumbai Indians in the IPL auction on Saturday – scored 23 from 25 balls.
In reply, the Knights were bowled out for 124 in 19 overs.
Farhaan Behardien top-scored with 31 off 27 balls, while Lizaad Williams, Aaron Phangiso and Tabraiz Shamsi each took two wickets for the Titans.
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