Five-time champions Toulouse face a home quarter-final next weekend against English side Exeter while Northampton will host the Pretoria-based Bulls.
Toulouse, who were bolstered by the presence of France's preferred half-back pairing of Antoine Dupont and Romain Ntamack, the latter making his first appearance after eight months out injured, were outstanding as they stretched Racing from the start at the Stade Ernest-Wallon.
The visitors lost South African World Cup-winning captain Siya Kolisi, also making a comeback after a month out with a finger injury, after just 22 minutes when the flanker hobbled off with what appeared to be an ankle injury.
France hooker Peato Mauvaka opened the scoring after just five minutes with wing Matthis Lebel adding the second try six minutes before the break.
With Blair Kinghorn, preferred as kicker to Ntamack, missing both conversions, Toulouse only led 10-0 at the break but quickly asserted themselves with a third try after 55 minutes when Dupont teed up centre Paul Costes, a first-half replacement for Pierre-Louis Barassi.
Pita Akhi added a fourth 10 minutes from time and, after Eddy Ben Arous touched down for the Parisians, Alexandre Roumat completed the scoring with the fifth Toulouse try in the last minute.
Hendy double
Northampton booked their place with a hard-fought 24-14 win over Munster at a windy Franklin's Gardens, thanks to two tries in the last quarter from replacement winger George Hendy.
In a repeat of the 2000 final, which the Saints won 9-8, the teams were locked at 14-14 at half-time before Hendy's intervention.
"Munster came out of the blocks really strong and that defensive set at the start of the game helped us go and win the game," Northampton's Curtis Langdon told ITV.
"Defence is something we have gone really hard at this season.
"We are just taking every game as it comes and it is brilliant to have this atmosphere. We just want to keep it going."
James Ramm, who scored twice against Saracens in the Premiership last week, continued his form with the opening try but Munster wing Sean O'Brien replied shortly after.
Munster were dominating and Mike Haley put them ahead with Munster's second try but just before half-time Tommy Freeman raced over to tie up the scores at the break.
The second half produced more quality rugby with Northampton slowly taking control of the arm-wrestle, reclaiming the lead with the first of Hendy's tries on the hour.
The move started from a line-out inside Saints' 22 with Fin Smith feeding Ollie Sleightholme with a delayed pass before Ramm sent Hendy over.
The wind caused Smith to miss the conversion and then a penalty attempt but Hendy sealed the tie seven minutes from time when he broke two tackles to touch down in the left corner.
"We can't fault the effort as that was there," a disappointed Munster captain Tadhg Beirne told ITV.
"We were against the wind in the second half and knew we would have to battle it out. Credit to Northampton, they were better on the day."
Quarter-finals (GMT)
Saturday April 13: Bordeaux-Begles (FRA) v Harlequins (ENG) (1400), Leinster (IRL) v La Rochelle (FRA) (1630), Northampton (ENG) - Bulls (RSA) (1900)
Sunday April 14: Toulouse (FRA) v Exeter (ENG) (1400)
