The Romanians, who grabbed a famous victory over Roma in Italy two weeks ago, produced another resilient performance to dent the Blues a second win in Group A.
Chelsea's casualty though might be the injury of marksman Didier Drogba, who was stretchered off in agony late in the second half.
The Ivorian, who has just recently recovered from a serious knee problem, slipped awkwardly as he appeared to have aggravated the injury.
Baptista Show
Roma came back from a goal down to beat ten-man Bordeaux 3-1 at home, thanks to a second-half brace from substitute Baptista.
Johan Gourcuff put the home side in front with a powerful shot in the 18th minute, but the French side were reduced to ten men as Carlos Henrique saw red before half-time.
Mirko Vucinic put Roma back in contention with a fine header in the 64th minute, before Baptista gave the Italians the lead with a superlative freekick.
The Brazilian concluded the victory with a close tap-in eight minutes from the end to help the Giallorossi make up for their embarrassing first-day defeat.