A stoppage-time Patrik Schick equaliser spared Leverkusen's blushes last week in Baku, and also maintained their unbeaten record this season, after Qarabag took a shock 2-0 lead against the runaway Bundesliga leaders.
"Maybe it's true that the result is more fortunate for us than for Qarabag. Great respect, they perhaps deserved a better result," said Leverkusen coach Xabi Alonso after the first leg.
Despite the surprise 2-2 draw, Leverkusen showed no sign of slowing down in their pursuit of silverware at the weekend as they immediately bounced back with a home win against Wolfsburg in the league.
The form team in Europe now boast a record of 31 wins and five draws across all competitions this season, making them the first Bundesliga side to go without defeat in 36 consecutive matches.
As the search for Leverkusen's first silverware in over 30 years reaches the business end of the season, Alonso and his charges will not want this momentum to stop abruptly at match 37 against the Azerbaijani champions.
However, after going toe-to-toe with the Germans for 91 minutes last week, Qarabag will arrive at the BayArena believing that anything is possible.
Alonso said the Baku club "have quality players who are capable of playing in the top leagues" and they will be keen to continue to showcase their talents on the European stage.
Qarabag coach Gurban Gurbanov is confident his team can step up and perform at an even higher level than in the first leg: "I'll prepare the team to play even better in Germany."
Leverkusen's fellow tournament favourites Liverpool will likely have an easier ride on Thursday at Anfield after dispatching opponents Sparta Prague 5-1 last week.
Liverpool were boosted by the return of Mohamed Salah in the first leg but with the tie all but sewn up already, it is likely manager Jurgen Klopp will give more playing time to the squad's youngsters.
On the south coast of England, Brighton have it all to do against Daniele De Rossi's in-form Roma following a comprehensive 4-0 defeat in the Italian capital last week.
Bubble-bursters Freiburg?
German side Freiburg take a 1-0 lead to West Ham but will still need to defy the Hammers' impressive home record in Europe to progress to the quarter-finals.
Europa Conference League holders West Ham have won all 10 of their last 10 European games at the London Stadium, going back over the last two seasons.
Michael Gregoritsch's goal in the last 10 minutes gave Freiburg a slender lead after West Ham "didn't have (their) shooting boots on", according to manager David Moyes, and squandered chances to break the deadlock in Germany.
Moyes is counting on this home form to help his wasteful side find the target and overturn the deficit.
"We'll do everything to try and turn it around. We'll have our crowd and atmosphere behind us," said the Scot.
Rangers host Benfica with the tie all to play for following an entertaining 2-2 draw in Lisbon.
A resolute defensive display last week by Rangers frustrated Benfica and a similar performance on Thursday at Ibrox could well see the Portuguese champions exit at the hand of the 2022 Europa League finalists.
Sporting Lisbon will visit Italians Atalanta on a level playing field after holding the visitors to a 1-1 first-leg draw, despite Atalanta hitting the post three times in the match.
Italian giants AC Milan go to Slavia Prague with a two-goal buffer, after winning 4-2 at the San Siro, and Marseille make the trip to Villarreal sitting four goals to the good following a dominant first-leg display against the Yellow Submarine.
In the Europa Conference League, Fiorentina host Maccabi Haifa after their last-gasp 4-3 win in Budapest and it is all to play for at Villa Park after Aston Villa and Ajax's goalless draw last week.
