Leverkusen, the Bundesliga champions who have also reached the May 25 German Cup final, played their 49th match without defeat in all competitions, surpassing Benfica's long-standing European record set from 1963 to 1965.
Atalanta's passage to the Dublin final, where they will face Bayer Leverkusen, later this month was fully deserved after a dominant performance in which Marseille barely had a kick in yet another poor away display from the Ligue 1 outfit.
Xabi Alonso's Leverkusen, who have 40 wins in their unbeaten run, face Atalanta in the May 22 final in Dublin after the Italians comfortably got past Olympique Marseille.
Xabi Alonso's rampaging Bayer Leverkusen will have an additional incentive in Thursday's home second-leg Europa League semifinal against Roma: breaking a 59-year-old European football record.
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Leverkusen's superiority was fully on display.
"Disappointed that we did not go through but not frustrated or angry. Now we can focus on the league and that's what we will do," Klopp told reporters.
Last season's runners-up Roma advanced to their fourth European semi-final in a row.
Atalanta have a chance to make history on Thursday as they welcome Liverpool to Bergamo with one foot in the Europa League semi-finals thanks to a stunning first-leg win at Anfield.
"It just was a really bad game, oh my god. We started well, really well, and then didn't continue. I think even before they scored, we just lost the plot a little bit, we were everywhere and nowhere," Klopp told reporters.
Atalanta knocked out Portuguese side Sporting Lisbon in the previous round but have won just two of their last nine matches in all competitions.
Leverkusen head into Thursday's home first leg against West Ham in the Europa League quarter-finals unbeaten in 41 matches this season, with 36 wins and five draws.
Jurgen Klopp's Liverpool, who are still in contention to win a quadruple this season, will entertain Atalanta at Anfield on April 11 and go to Italy a week later for the return.
AC Milan, Marseille, Roma and West Ham were among the other sides to also book their place in Friday's quarter-final draw.
Liverpool remain on course to send Jurgen Klopp off with a quadruple.
Mohamed Salah has given Liverpool a major boost after the Egypt star travelled to Sparta Prague for Thursday's Europa League clash following his recent injury lay-off.
AC Milan, meanwhile, were drawn against French club Rennes.
A youthful Liverpool side lost 2-1 at Union Saint-Gilloise in their final Europa League group game on Thursday, while Villarreal snatched a place in the last 16 from Rennes with a dramatic victory in France.
Jurgen Klopp's side sealed top spot in Group E thanks to Gakpo's brace and goals from Luis Diaz and Mohamed Salah at Anfield.