Delev fires CSKA Sofia into semis
Striker Delev put the home side in front in the 34th minute after he and captain Todor Yanchev sliced open the Cherno More defence.
Delev then turned provider in the 67th minute as Brazilian Marquinhos doubled CSKA's lead.
The visitors went down to 10 men midway through the second half when defender Alexander Alexandrov was sent off for a second bookable offence.
The other three quarter-finals are on Wednesday and Thursday. Denmark's Lars Christoffersen will referee the highly-awaited clash between league leaders Litex Lovech and second-placed Levski Sofia.