The Chiefs did their best to produce a stunning comeback, but the Reds held on to secure a hard-fought victory.
The Reds finally ended the wait for an Australian win in the Super Rugby Trans-Tasman season, but there were heavy defeats for the Waratahs and the Brumbies on Saturday.
With Damian McKenzie sent off in the 22nd minute for making contact with the head area, the impressive Reds appeared to be coasting to victory when they opened up a 40-8 lead midway through the second half.
Isaac Henry scored two of their six tries, the first of which came with Chase Tiatia in the sin bin. McKenzie's red card then swung the game even further in the Reds' favour, as they capitalised on having an extra man to run up the score.
However, they were then forced to repel a frenetic comeback bid, four tries from the Chiefs closing the gap down to six points in the closing minutes.
The hosts managed to hold on to win 40-34 and register a first Australian success in the tournament at the 15th attempt, in the process denting their opponents' hopes of making the grand final as they collected only a losing bonus point.
New Zealand sides had dominated the two earlier fixtures, though, including the rampant Crusaders cutting loose against the Waratahs.
There were eight different try-scorers for Scott Robinson's team in an emphatic 54-28 triumph, with Richie Mo'unga converting all bar one of the scores in the rout.
The Waratahs did get within 10 points after Izaia Perese touched down with Oli Jager in the sin bin, while they also capitalised on yellow cards for David Havili and Nathan Vella to score a late try through Alex Newsome, albeit it was no more than a consolation effort.
The Blues made it three straight Trans-Tasman wins despite a determined Brumbies side matching them in the first half at Eden Park, the away team even holding a 10-7 lead when hooker Connal McInerney went over.
They were unable to hold onto the lead for long and trailed 17-10 at the break, Finlay Christie touching down for a try converted by Otere Black, who also slotted over a penalty.
The hosts added 21 points without reply in the second half, Bryce Heem, AJ Lam and TJ Faiane all grabbing tries in a 38-10 triumph that sees them take over at the top of the table.
