Investec Champions Cup
Toulouse (24) 43
Tries: Capuozzo, penalty try, Brennan, Thomas, Remue 2, R Ntamack Cons: R Ntamack 3
Exeter Chiefs (26) 40
Tries: Wimbush 3, Yeandle, Varney, Butt Cons: Slade 5
Toulouse denied Exeter Chiefs a famous Champions Cup victory in France, fighting back to win a frenetic pool game with 14 men following Rodrigue Neti's first-half red card.
Exeter had the chance to force a draw but, with the clock in the red, Henry Slade missed a penalty from about 40 metres out.
Zack Wimbush, starting on the wing for Exeter in place of injured England international Immanuel Feyi-Waboso, scored a hat-trick of tries as the 2020 champions fell just short of winning a classic contest.
Wimbush had put Exeter ahead early, but Toulouse led 12-7 when prop Neti was dismissed in the 16th minute for making shoulder-to-head contact in a tackle on Ross Vintcent.
That incident came during a frantic first half which ended 26-24 in Exeter's favour and included eight tries - four for each side - as well as two yellow cards.
The lead swapped hands several times after the break, but Toulouse grabbed the advantage while Exeter's Ben Hammersley was in the sin-bin to take a narrow victory.
Wimbush's second-minute score stunned the home crowd, but Toulouse replied quickly through Italy's Ange Capuozzo and a penalty try, which also resulted in Exeter full-back Sam Harris being sent to the sin-bin.
Wimbush scored again soon after Neti's early exit, before tries from Joshua Brennan and Teddy Thomas moved Toulouse 10 points in front.
Back came Exeter, now two men to the good after Thomas was yellow-carded for a deliberate knock-on, as Jack Yeandle burrowed over and Stephen Varney touched down under the posts.
After the interval, Will Butt capitalised to extend Exeter's advantage to nine points when Antoine Dupont's clearing kick was charged down, but that was quickly wiped out by some wonderful attacking play by the hosts.
Although Wimbush grabbed his third, Matias Remue's double and another try by Romain Ntamack established a three-point lead for the home team.
There was more drama to follow as Exeter were awarded a late penalty and the visitors went for the posts, but centre Slade pulled his kick just wide, so Exeter had to settle for just a losing bonus point.
Toulouse: Remue; Thomas, Gourgues, Chocobares, Capuozzo; R Ntamack, Dupont (capt); Neti, Lacombre, Aldegheri, Brennan, Merkler, Cros, Elias, T Ntamack.
Replacements: Mauvaka, Bertrand, Colombe, Bonnard Martin, Jelonch, Kouassi, Graou, Menoncello.
Exeter: Harris; Wimbush, Slade, Butt, Wyatt; Skinner, Varney; Goodrick-Clarke, Yeandle, Iosefa-Scott, Hooper, Jenkins (capt), E Roots, Vintcent, Fisilau.
Replacements: Gulley, Burger, J Roots, Wilson, James, Wolstenholme, Haydon-Wood, Hammersley.
Referee: Hollie Davidson (Scotland)
Assistant referees: Rob McDowell (Scotland) and Finlay Brown (Scotland)
TMO: Dave Sutherland (Scotland)