The win ensured Barca go through to the last 16 in first place in Group E. They have 13 points from five games, Roma and Bayer Leverkusen both have five and BATE Borisov have four.
Barcelona are in the last 16 for the 12th consecutive season following another blistering attacking display that comes hot on the back of their 4-0 destruction of Real Madrid in La Liga last Saturday.
Gerard Pique and Adriano also scored for Barcelona with Roma striker Edin Dzeko, who had a penalty saved, netting a consolation goal in stoppage time.
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(Reporting by Tim Hanlon; editing by Rex Gowar)
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