Maurizio Sarri's men came into the match only needing a draw to progress into the next stage of the competition after a narrow 1-0 away win in the first leg last week.
The Blues raced into a 3-0 lead within the opening 20 minutes of the match through Pedro Rodriguez, Olivier Giroud an own goal from by Simon Deli.
The away side pulled one back in the 26th minute when Tomas Soucek fired a bullet header into the top right corner before Pedro added his second of the night a minute later to give the Blues a commanding 4-1 lead at the break.
The second half started on a high note just like the first opening 45 minutes with Slavia scoring two quickfire goals in a span of five minutes (51 and 55) through Petr Sevcik to make it 4-3 and threaten to turn the tie on its head.
However, the pace of the game dropped significantly after the two goals and neither side could get another goal.
Chelsea have now set up a date with Bundesliga side Eintracht Frankfurt in the semi-finals.