Chiefs will face Hurricanes in the Super Rugby semi-finals after the former's impressive victory at Stormers on Saturday.
Last season's losing finalists Hurricanes hammered Sharks 41-0 earlier in the day, before Chiefs put in a stunning attacking performance to prevail 60-21 at Newlands Stadium.
The other semi-final pits defending champions Highlanders - 15-9 winners over Brumbies on Friday - against Lions, who ran out 42-25 victors over Crusaders a day later.
Chiefs fell behind to an early Vincent Koch try, but that was as good as it got for Stormers, as the visitors ran in four scores before the break.
Sam McNicol was the first go over, before a stunning step from Brad Weber sent him across the whitewash. Aaron Cruden then charged down a kick and, following a defensive fumble, Tom Sanders dropped down for Chiefs' third.
Better was to come as James Lowe's remarkable kick and chase close to the left touchline resulted in Chiefs taking a 34-7 lead, although Koch did barrel over for his second shortly before half-time.
After Damian McKenzie's try further extended the advantage following the restart, Nizaam Carr's late score looked to have restored a measure of pride for the hosts, only for Hika Elliot, Tevita Koloamatangi and Tawera Kerr-Barlow to all touch down in the final four minutes to seal a resounding success.
At Ellis Park, Lions ran in five tries in their victory, while Elton Jantjies kicked 17 points.
The home side led 22-10 at the interval and although Crusaders put up a fight, scores in the final 10 minutes from Ruan Combrinck and Ross Cronje set up Lions' last-four meeting with Highlanders.