Having played out a goalless draw in the first leg in Moldova, the tie was wide open ahead of Friday's decisive encounter.
However, the Bulgarian hosts soon set about putting the tie beyond any doubt.
French defender Jackson Mendy put Litex ahead after 27 minutes, and matters soon got worse for the visitors as they were reduced to 10 men.
Defender Dumitru Bacal was the man to see red for Veris for a second bookable offence.
And the man advantage eventually told, Colombian attacker Gil doubling Litex's lead in 63 minutes before putting the gloss on the performance 11 minutes later.
Litex will now face Hungarian side Diosgyor in the next round.
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