Bryan Cristante was shown his marching orders midway through the second half, just as Paulo Fonseca's side were looking to get back on level terms in the contest.
Musa Barrow scored twice for the visitors either side of half-time, after Riccardo Orsolini had originally opened the scoring.
A Stefano Denswil own goal briefly got the Giallorossi back on level terms, before Barrow made his presence known.
Henrikh Mkhitaryan - returning to the starting line-up after injury - then headed home Bruno Peres's cross to give Roma hope, before Cristante's red card took the wind out of the side's sails.
Roma are back in action next Saturday, as they face Atalanta in Bergamo in another important game in the race for the top-four.
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