Willian stepped up to fire in from 20 yards with Kovacsik’s poor positioning leaving him unable to get across to save his free-kick and putting Chelsea ahead.
He did not need to lament the error for long, Marko Scepovic’s flick-on from a corner fell at chest height for Ampadu, who awkwardly headed a corner into his own net at the other end.
Chelsea’s luck continued to run against them when Morata, a largely peripheral figure, went down clutching his left knee in innocuous circumstances before the break and was replaced by Giroud.
The hosts turned the game on its head 11 minutes after the restart, when Milanov’s excellent delivery found Nego at the back post, and he connected sweetly with his volley to leave Caballero with little chance.
Giroud failed to capitalise on either of two good opportunities that initially came his way, but the France striker made amends in the 75th minute, mirroring Willian’s earlier set-piece wizardry to seal a share of the points.
Chelsea had won their opening five Europa League games and are joined in the knockout stages by Bate Borisov, who beat PAOK Salonika in the other game. Vidi could have qualified – but needed to better the Belarusian side’s result.
Next Chelsea will travel to Brighton at 13.30pm on Sunday, fresh from ending Manchester City’s unbeaten league record last weekend.