Northampton Saints will have to try again next week. By dint of Harlequins losing to Wasps their defeat here in Exeter brings them back to Sandy Park for the play-off semi-final on Saturday.
Curiously they go into it as the worst fourth-placed team in Premiership history, with only 56 points - lower than London Irish and Leeds' tally of 57 in 2002 and 2003 respectively.
But they come with hope. Here they stretched and troubled Exeter, who ended the league season top for the second consecutive season and with 86 points - just one short of the record set by Saracens in 2014.
Despite suffering defeat at Exeter, Northampton will face them again in Premiership play-offs
England centre Henry Slade set Exeter on the way to victory by scoring the opening try
EXETER CHIEFS: Nowell; Cuthbert, Slade, Devoto, Woodburn; J Simmonds, White; Moon, Yeandle (capt), Williams, Dennis, Hill, Ewers, Armand, Kvesic
REPLACEMENTS: Cowan-Dickie, Keast, Francis, Skinner, S Simmonds, Maunder, Steenson, Hill
TRIES: Slade, Moon, Armand, Kvesic, Dennis, Cowan-Dickie
CONS: J Simmonds 5
NORTHAMPTON SAINTS: Tuala; Collins, Hutchinson, Francis, Naiyaravoro; Biggar, Reinach; Waller (capt), Marshall, Hill, Moon, Lawes, Gibson, Ludlam, Harrison
REPLACEMENTS: Fish, van Wyk, Franks, Ribbans, Wood, Mitchell, Grayson, Burrell
SIN-BIN: Lawes (40 mins), Waller (40 mins)
TRIES: Francis, Hutchison, Reinach
CONS: Biggar 3
REFEREE: Karl Dickson.
Chiefs might be worried. Only 31 per cent of league-toppers win the title, and Northampton - who scored through Piers Francis, Rory Hutchinson and Cobus Reinach - are dangerous.
However, when Exeter found their rhythm and kept the ball for large periods they looked that too. Tries from Henry Slade, Ben Moon, Don Armand, Matt Kvesic, Dave Dennis and Luke Cowan-Dickie meant they took a bonus-point win.
If Rob Baxter thought his Exeter Chiefs were in an 'emotional vacuum' after securing a home semi-final slot last month they were in danger of being dragged into a black hole after half an hour here.
Since having not much to play for Exeter have lost to Wasps at home, snuck past Harlequins unconvincingly and then been hammered by Saracens with a rotated team.
And here their fully-loaded XV were 14-7 down and struggling. Northampton's first try came from a beautiful Dan Biggar pass -