The Cobras had no trouble chasing the total down inside the 16-over mark - the requirement to pick up a bonus point - as their top three all contributed.
Richard Levi and Andrew Puttick provided the roaring start, taking 62 off the first five overs, and after Levi had been dismissed for a 23-ball 44, Puttick and Omphile Ramela were able to slip into cruise control.
While Ramela got out for 28 with the target in sight, Puttick finished unbeaten on 48 from 39 balls as the Cobras got home in 15.4 overs to win by eight wickets.
George Linde had been the man to spark the Dolphins collapse as he had Divan van Wyk caught at long leg, but it was Engelbrecht who claimed the key wickets of Cameron Delport (46) and Dwayne Bravo.
Engelbrecht finished with figures of 3 for 19 from his four overs, while Shezi finished with 3 for 23 after picking up the wickets of Vaughn van Jaarsveld (28) and Sibonelo Makhanya to prevent any late Dolphins assault.
Engelbrecht walked away with the Ram Deliverer of the Day prize, while Levi was named Ram Slammer of the Day.