Eintracht, who travel to Chelsea on Thursday with the tie level at 1-1, left star striker Jovic on the bench at BayArena.
But Leverkusen recorded a ruthless victory to move level on points with fourth-placed Eintracht as the race for Champions League qualification continues with just two games remaining.
Peter Bosz's hosts were 2-0 up after just 13 minutes, with Kai Havertz's opener followed up by Julian Brandt.
Filip Kostic swiftly reduced the deficit but the Leverkusen onslaught continued and it was 6-1 by the 36th minute.
Lucas Alario struck twice with Charles Aranguiz also on target before Martin Hinteregger's own goal completed the scoring.
6 - @bayer04_en have tied the #Bundesliga record, scoring six goals in the first half. The last team to do this were Borussia Mönchengladbach in April 1978 when they beat Borussia Dortmund 12-0 (6-0 at half-time). Sixpack. #B04SGE pic.twitter.com/E1k07U39yH— OptaFranz (@OptaFranz) May 5, 2019
Never before have Die Werkself scored four goals inside 28 minutes in the Bundesliga and it was the first time they had scored five or more in the first half of a game.
The hammering was new territory for Frankfurt, too, who have never previously conceded six goals before half-time.
Eintracht head coach Adi Hutter appeared to rue his team selection, sending on Jovic and Mijat Gacinovic before half-time.
But Hutter's side will have to justify his decisions when they head to Stamford Bridge to take on Chelsea for a place in the Europa League final.
They will be backed by a sizeable, noisy away following in London, and the crowd will be demanding a signficantly better performance than Sunday's shambles.
Hutter's team are aiming to replicate the success of the club's 1979-80 side who won the UEFA Cup, their only European title to date.
They require at least one away goal against the Blues to stand any chance of progression.