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Juan Mata went close to making it 2-0 to the Premier League outfit on the half-hour mark when he was set up by Oscar, but the Spanish midfielder's shot lacked power and was easily saved by Tatarusanu.
Chelsea did double their lead on the stroke of half time, thanks to an own goal from Daniel Georgievski. Eto'o took a shot on the Steaua goal that Tatarusanu parried straight at the defender and saw the ball fly into the net.
The 2012 European champions made it 3-0 10 minutes into the second half when Ramires found the target again.
Schurrle turned past his defender on the left, cut inside and played the ball to Oscar, who set up the Brazilian midfielder for his second goal of the evening.
Oscar was unlucky not to score Chelsea's fourth goal in the 67th minute when he saw his shot from 20 yards come back off the crossbar.
Frank Lampard made it 4-0 to Chelsea in the 90th minute when he rifled an effort home from 18 yards.