The win left Claudio Ranieri's side in sixth place on 62 points, behind AC Milan on their head-to-head record.
Surprise package Atalanta climbed to third with 65 points thanks to a 2-1 home win over relegation-threatened Genoa.
The defeat came on the day that Juventus displayed their new strip which no longer features the club's iconic black and white stripes in a breakaway from over a century of tradition.
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Eyebrows were raised when Manchester City striker Aguero, addressing a question in front of gathered media, indicated the next Ballon d'Or victor has "to be in the Champions League [final]".
Playing in their new jerseys, Juventus with nothing left to play for, and with growing speculation over Allegri's future, failed to take advantage of their first half domination.
Roma goalkeeper Antonio Mirante made brilliant early saves to deny Juan Cuadrado and Paulo Dybala before Lorenzo Pellegrini hit the bar for the home side. Then in added time, it was Edin Dzeko who killed off the game by making it 2-0. Sassuolo played more than an hour of the match with 10 men after Mehdi Bourabia was shown a second yellow card for celebrating his goal by half removing his shirt and was sent off.