Morkel slammed four fours and five maximums in his 57 not out off 28 balls.
The Paarl side, who got to their target in 15.2 overs, will now go on to face the Jozi Stars in the Qualifier on Friday.
Rassie van der Dussen and Dan Christian produced a 118-run partnership which powered the Stars to 239/3.
It was only a second win of the campaign for them. Though, they remained rooted at the end of the points table.
In reply, a 120-run stand between Du Plessis, who made 61 off 34 balls, took them too far ahead for the Stars
Cloete struck 65 from 59 balls which laid the foundation for the Spartans’ 165/4 in their total of 20 overs.
The Proteas opener smashed three sixes and 12 fours in his 47-ball cameo as the hosts chased down a 145-victory target with 4.3 overs to spare.
Two consecutive sixes in the final over from Jozi Stars’ Nono Pongolo saw his side to a one wicket win over the Durban Heat
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