Barca won a penalty early in the second half when Luis Suarez was fouled and Messi converted to put the league leaders in front and the Uruguayan forward made sure of the points with a simple finish from close range in the 82nd minute.
Croatia beat Russia 4-3 in a penalty shootout after a dramatic 2-2 draw on Saturday, ending the World Cup hopes of the host nation and advancing to a semi-final against England.
Both Argentinian and French coaches see Lionel Messi as a key player in the round-two knockout game and are strategising with him in mind.
The pair of own goals by Daniele De Rossi and Kostas Manolas plus some sloppy defending that allowed Gerard Pique and Luis Suarez to also score left Roma on the verge of elimination.
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