Ben Tameifuna's second-half double ensured the visitors pulled away after the Blues had, despite flanker Kane Barrett's 22nd-minute dismissal, remained level at the break.
The Chiefs twice crossed the whitewash in the first half, through Bundee Aki and Hikawera Elliot, but a reply from Charles Piutau and eight of Baden Kerr's 11-point match haul made it 13-13 at half-time.
But Kerr was sin-binned after half-time, leaving his side down to 13 men, and Tameifuna cashed in for the first of his tries to break the game open.
The Reds held off the fast-finishing Waratahs 14-12 to record an ugly win and book a qualifying final match-up with the Crusaders in Christchurch next weekend.
Queensland were forced to play from behind after conceding two tries from Cam Crawford and Berrick Barnes before the break but hit the front in the 56th minute after two penalty goals from Quade Cooper. Ben Lucas crossed for the Reds.
The Waratahs produced error after error in arguably their worst performance of the season but had their chances to steal victory in the final 10 minutes.
Barnes missed a sideline penalty goal in the 79th minute and followed it up with a botched drop goal after the siren to finish a season of progress on a sour note in front of 26,037 fans.
The Western Force have finished their disappointing season with a shock 21-15 win over the finals-bound Brumbies at nib Stadium in Perth.
The Force were easily the most impressive of the two sides in the first half and they profited from tries to skipper Matt Hodgson in the 22nd minute and number eight Ben McCalman on the stroke of half-time to take a handy 14-3 lead into the break.
The first half was without doubt the Brumbies' worst opening 40 minutes of the season, with the Australian Conference leaders making no less than nine handling errors, missing 13 tackles and offering up 10 turnovers.
It was not much of an improvement for the visitors in the second half, but they did post a couple of tries to at least get within range of the Force.
The result means the Brumbies finish the home-and-away rounds in third position in the table, confirming a finals clash with the sixth-placed Cheetahs at home next weekend.
The Sharks scored 10 tries and notched 32 unanswered second-half points as they thrashed the Southern Kings 58-13 in a clash where there was only pride to play for.
Marcell Coetzee, Bismarck du Plessis, Odwa Ndungane, Riaan Vijoen, Tendai Mtawarira, Louis Ludik, Keegan Daniel, Fred Zeilinga and Meyer Bosman all touched down for the home side, who were also awarded a penalty try after the Kings deliberately collapsed a driving maul. Bosman kicked four conversions.