The hosts - enjoying the bulk of possession and territorial advantage in the first half - were clinical at the start of the game, both on defence and attack, where they managed to vary their play to cause the DHL Stormers some issues.
To compound matters for the visitors, they slipped too many tackles, their tactical kicking wasn't up to scratch and their discipline was also lacking a bit. As a result, the Chiefs scored three converted tries in the first 30 minutes as their speedsters Tom Wyatt, Jack Nowell and Olly Woodburn went over.
Wyatt's try came from a pin-point cross kick after the Capetonians' defence was stretched; Nowell left two tacklers in his wake as he sniped around a ruck; and Woodburn rounded off a clever move off the back of an attacking lineout.
The DHL Stormers started the second half with more purpose, but it was England No 8 Sam Simmonds who stretched Exeter's lead to 28-0 with a try that exploited some more weak defence from the visitors.
The Capetonians refused to give up though and when Damian Willemse (fullback) scored their first try in the 53rd minute, there was a spring in their step.
Ruhan Nel (outside centre) went over six minutes later, but the TMO spotted obstruction earlier in the move. That didn't stop the DHL Stormers though and Suleiman Hartzenberg (wing) scored their second try from a clever kick by Herschel Jantjies (scrumhalf) in the 61st minute.
Unfortunately flyhalf Manie Libbok missed both conversions, and Exeter's lead remained more than two converted tries with time running out. The hosts didn't flinch either, and despite the DHL Stormers flurry, they remained focused on the task at hand, sticking to their guns until Jack Yeandle (replacement hooker) was driven over in the 74th minute to all but seal the deal.
Marvin Orie (lock) got his name on the score-sheet win the 77the minute from a charge down and after a long deliberation with the TMO, the referee awarded the try, which Libbok converted, but it was too little, too late for the holders of the Vodacom United Rugby Championship, especially after Tom Cairns (replacement scrumhalf) got a sixth try for the hosts shortly thereafter.
Exeter Chiefs 42 (21) - Tries: Tom Wyatt, Jack Nowell, Olly Woodburn, Sam Simmonds, Jack Yeandle, Tom Cairns. Conversions: Joe Simmonds (6).
DHL Stormers 17 (0) - Tries: Damian Willemse, Suleiman Hartzenberg, Marvin Orie. Conversion: Manie Libbok.