Fullback Josh Ioane put the Chiefs on the board with the first try in the 12th minute, scoring on the backof some consistent driving play by the pack and then an inside cut to cross.
But the Reds responded quickly, going to their lineout drive for hooker Matt Faessler to cross four minutes later.
Two good runs by winger Suliaisi Vunivalu created the Reds’ second try, the first giving them good field position and the second providing room down the blindside with inside support from No. 8 Harry Wilson and flanker Fraser McReight, who scored.
Chiefs flanker Simon Parker charged down a Vunivalu clearance in the 46th minute.
The Chiefs pounced, with the ball worked to the right flank, where wing Shaun Stevenson got across in the corner.
But a kick into the Chiefs’ 22 by replacement back Harry McLaughlin-Phillips produced a wicked bounce that beat Ioane and was taken by Reds wing Mac Grealy, who found centre Josh Flook inside to score the match-winning try with 24 minutes left.
But that was only an entree to a thrilling finish, with McLaughlin-Phillips sealing the win with a penalty turnover 5 metres from his line after a 23-phase Chiefs assault on the line.