Ignacio Mieres scored a last-minute try to hand Exeter victory and cap a remarkable fightback which saw them overturn a 23-7 half-time deficit.
Tries from prop Henry Thomas and centre Sam Tuitupou, along with two conversions and three penalties from Nick MacLeod, gave the hosts a commanding lead.
It was just reward for their bold attacking approach, yet Exeter hit back with a 22nd-minute try from Richard Baxter and were a transformed side after the restart to keep Sale scoreless during the second period.
After Thomas was sinbinned for Sale in the 55th minute, Exeter went on to claim a penalty try, which Argentinian playmaker Mieres converted to cut Sale's lead to three points.
The replacement fly-half then kicked a penalty to level the scores in the 72nd minute and scampered clear in the last minute after intercepting an errant Sale pass to give the visitors victory.
Exeter had won at Edgeley Park in Sale's final home game last season but they struggled during the opening exchanges as the hosts made a vibrant start. With scrum-half Dwayne Peel and fly-half MacLeod dovetailing effectively, Sale were brimming with creativity behind their dominant pack.
Two well-taken penalties from MacLeod put them 6-0 ahead inside the opening seven minutes and they soon had the game's opening try two minutes later.
A quick line-out led to full-back Rob Miller collecting possession just inside the Exeter half and, with a combination of searing pace and delightful footwork, he outstripped a clutch of visiting defenders to race deep into the Chiefs' 22-metre line.
Miller then showed intelligence to spot Thomas in support to his right and his neat inside pass allowed the supporting prop to crash over the line. MacLeod added the extras and Sale went close again moments later when a loose ball was almost grounded by a home player.
Sale did score their second try in the 18th minute, however, thanks to Peel's clever kick behind the Exeter defence, where Tuitupou had the speed and strength to collect possession and ground the ball.
Four minutes later, and from their first meaningful foray into Sale's 22-metre line, Exeter scored a try when a quick pass from Gonzalo Camacho allowed number eight Baxter to cross over the line. Gareth Steenson added the extras but Sale remained largely dominant and MacLeod's third penalty on the stroke of half-time sent them in at the break with a 23-7 advantage.
Steenson added a penalty for Exeter in the 51st minute but he then departed and was replaced by Mieres, who missed a penalty but then slotted one after Thomas was sinbinned for Sale.
The visitors began to pin Sale back towards their own line, with openside flanker James Scaysbrook a pivotal figure in their period of dominance. With Exeter in control, they earned a penalty try in the 65th minute which Mieres converted to leave the scores finely poised at 23-20 in Sale's favour.
MacLeod then hit the post with a penalty to add to the tension before Mieres landed a penalty with eight minutes remaining to level the scores. There was still time for him to race clear in the dying embers for an interception try which he then converted as Sale were forced to settle for a losing bonus-point.