Saints suffered last-gasp heartache at Sandy Park as Exeter Chiefs snatched a dramatic 31-30 win from the final play of the game.
Thomas Waldrom's try and Joe Simmonds' conversion secured the victory for the home side, who were 30-17 down with 10 minutes remaining.
Tries from Rob Horne, Ben Foden and Harry Mallinder, plus points from the boots of Piers Francis and Stephen Myler, had put Saints in control.
But Exeter battled until the end, with Don Armand's try sparking them into life and Waldrom's effort helping to end the Chiefs' three-match Aviva Premiership losing streak.
It means Saints have now lost on their past six visits to Sandy Park, with the black, green and gold's most recent victory at the ground coming in February 2014.
But they have every right to feel hard done by as they defended stoically for long periods and scored three fine tries.
Saints had started with real belief and after a strong opening 10 minutes, it was they who struck the first blow.
Lovely combination play on the left wing saw Jamie Gibson set up Australian centre Horne for the try.
Francis converted with ease to make it 7-0, but Exeter were soon threatening to issue an immediate riposte.
And after the home side kicked to the corner, the lineout drive proved too heavy to handle, with referee Christophe Ridley awarding a penalty try to the hosts.
Campese Ma'afu was sin-binned for his part in it and Saints' good early work had been undone.
Exeter then started to play with real pace, flying at Saints from all angles.
And it took some good work from Gibson and Francis to hold up hooker Luke Cowan-Dickie as he charged under the posts.
Francis was soon heading off for a head injury assessment and his replacement, Stephen Myler, made an impact early on, landing a long-range penalty as Saints reclaimed the lead.
Exeter were making an uncharacteristic amount of handling errors, with Saints quick to shut them down.
But the Chiefs were to take the lead for the first time four minutes before the break as Alec Hepburn just managed to reach the line and Gareth Steenson added the conversion.
However, it was to be a stirring response from Saints as Luther Burrell made a fine break, gave the ball to Horne and he offloaded to Foden, who sprinted to dive over in the corner.
Francis converted brilliantly from the left touchline and the black, green and gold had their lead back with a minute to go until half-time.
And Saints picked up where they left off early in the second half as a break involving Francis and Horne teed up full-back Mallinder for another fine try.
Francis converted with ease and Saints were 24-14 up, hunting the bonus point as the home fans fell silent.
Exeter responded with a Steenson penalty, but that was quickly cancelled out by a Francis effort at the other end after Ahsee Tuala won the restart and the Chiefs conceded a shot at goal.
Exeter were really struggling to get any attacking momentum with a stream of knock-ons costing them field position.
And when Saints got the chance to attack, they did, looking so sharp and forcing their hosts into conceding penalties.
Francis landed another kick to make it 30-17 with 20 minutes remaining and hopes of an away win were increasing by the second.
Saints produced an incredible defensive scrum in front of their own posts to push Exeter back towards the 22 and the Chiefs were being met with stern resistance at every turn.
The home side looked like they had run out of ideas, but Olly Woodburn made a break from nowhere and flanker Armand finished the move, sidestepping brilliantly to score.
Replacement fly-half Simmonds quickly took the conversion and the gap was just six points with more than nine minutes to go.
Exeter suddenly had their tails up with wave after wave of pressure heading towards the Saints line.
The home fans were now in full voice and Saints were submerged, having to scrap for every ball in their own 22.
Teimana Harrison was sin-binned with a minute to go after Exeter cranked up the heat with a lineout drive.
And after another penalty was kicked to the corner, Exeter went through the phases to push Waldrom over next to the right post.
Simmonds needed to hold his nerve to win it with the conversion, and he did, prompting jubilant home celebrations and leaving Saints shattered after a huge effort at Sandy Park.
Exeter Chiefs: Turner; Whitten, Devoto (Dollman 50), S Hill, Woodburn; Steenson (c) (Simmonds 68), Chudley (Townsend 68); Hepburn (Moon 50), Cowan-Dickie, Holmes (Street 78); Skinner (Lees 56), J Hill; Armand, Salvi (Kvesic 60), Waldrom.
Saints: Mallinder; Tuala, Horne, Burrell, Foden (Tuitavake 52); Francis, Groom (Reinach 72); Ma'afu (van Wyk 64), Haywood (Marshall 79), Brookes (Ford-Robinson 64); Paterson, Day (c); Gibson (Wood 60), Brüssow, Harrison.
Referee: Christophe Ridley