Record five-time Champions Cup winners Toulouse will play Harlequins, 42-41 victors over Bordeaux-Begles on Saturday, in the semi-finals.
Leinster, who dispatched two-time defending champions La Rochelle 40-13 in their quarter-final, take on Northampton in the other last-four clash on the weekend of May 4-5.
In scorching conditions in Toulouse, the home side were only a point ahead after a tight opening 40 minutes, but let rip with a totally dominant display in the second half.
"The first half was really hard and they came out pumping, but in the second half we managed to get our rugby on the field. This place was right behind us and it was awesome," Kinghorn told ITV.
"They are a good team, when they are on top they play front-foot rugby that is hard to stop, but we dealt with it well. In the second half we came alive."
Henry Slade opened the scoring with a penalty for Exeter.
Toulouse responded with a slick try, Romain Ntamack finishing off a move with Matthis Lebel providing the crucial pass.
Kinghorn booted the extras, Slade then kicked his second penalty before Ethan Roots crashed over for Exeter's first try from a close-range penalty move.
Kinghorn replied with a penalty. Slade hit his third on the half hour.
Toulouse flanker Jack Willis showed what England are missing by brushing off an attempted tackle by Harvey Skinner to find himself with a clear run to the line.
A Kinghorn conversion handed Toulouse a 17-16 lead at half-time.
The visitors regained the advantage as Slade hit his fourth penalty early in the second period.
The lead was short-lived as Kinghorn jinked his way over for try he also converted.
In a hammer blow for Exeter, Lebel again turned provider, breaking through from a line-out move and finding Pita Ahki on his inside.
Kinghorn converted and suddenly the home side were 31-19 up.
The Scot crossed for his second try after Paul Costes and Juan Cruz Mallia kept the ball alive.
In a disastrous 10 minutes for Exeter, Antoine Dupont was next on the scoresheet, the scrum-half displaying speed honed on the world sevens circuit to finish off a move started by a Willis burst.
Exeter grabbed their second try through replacement back Zack Wimbush before Argentina winger Mallia brought up Toulouse's half-century thanks to a long Ntamack miss pass.
Ahki scored his second try after another break from the outstanding Willis.
Mallia then bagged his second with Exeter dead on their feet, Thomas Ramos missing the conversion in the only blot on Toulouse's landscape in a remarkable display of rugby.
