The Waratahs struggled for possession and were hemmed in their territory for much of the game. But five of their six tries came from long range, with Folau and Hooper both grabbing two each.
The Chiefs still lead the competition on 42 points, but they could be passed by the Canterbury Crusaders (41), who face the Auckland Blues on Saturday. The Waratahs have 34 points and are five ahead of the ACT Brumbies in the Australian conference.
The Waratahs made a fast start, with Bernard Foley slotting an early penalty before Folau intercepted a long pass from Chiefs scrumhalf Brad Weber. He ran 90 metres for a try that gave his side a 10-0 lead inside 10 minutes.
The competition-leading Chiefs, who had been pressuring the Waratahs before Folau's try, put it straight back on the home side with Seta Tamanaivalu pouncing on a fumble behind the tryline by Nick Phipps.
The visitors then exploited the blind side six minutes later, as flyhalf Aaron Cruden strolled over untouched to level the score. Damian McKenzie gave the Chiefs a 13-10 lead they looked likely to hold until the break.
The Waratahs, however, stuck back again from long range. Wycliff Palu broke the line and Will Skelton then ran 25 metres before he fed Hooper to score under the posts and give the home side a 17-13 halftime lead.
The Chiefs retaliated in the second half, sending hooker Nathan Harris crashing over in the corner. But the Waratahs struck from deep twice in two minutes: both Kellaway and Hooper crossed to give their side a 31-18 lead.
Folau then grabbed his second after Phipps managed to squeeze out a pass close to the line, to give their side a 20-point lead.
Chiefs winger Toni Pulu then caught a delicate cross kick from flyhalf Cruden to reduce the deficit to 38-25. But Waratahs replacement Jack Dempsey scored with three minutes remaining and put the result beyond doubt.
Original source: Waratahs strike from long range to thump Chiefs