Inter’s clash with Bologna was suspended after the visitors failed to arrive having been placed into quarantine, meaning the Rossoneri’s win allowed them to close the gap at the top.
Second-placed Milan went ahead with Olivier Giroud’s eighth-minute penalty followed by Junior Messias’ 17th-minute strike.
Roma, who had two men sent off in the final 20 minutes, pulled one back before half-time from Tammy Abraham. But Rafael Leao sealed the points for Milan with an 81st minute goal.
These are important tests but only if we are able to repeat them next Sunday, continuity makes the difference in such a competitive and difficult league,” Pioli told reporters.
“We have a goal in mind which is to improve last years score and we started well. Now lets focus on the next game. In Serie A, either you are always at very high levels or you risk making a bad impression.
Elsewhere, third-placed Napoli were unable to close in significantly after a 1-1 draw away to Juventus.
Dries Mertens opened the scoring in the 23rd minute but Juve levelled early in the second half from Federico Chiesa.
Eighth-placed Lazio drew 3-3 with Empoli after trailing 2-0 early, while struggling Cagliari won 2-1 at Sampdoria and Verona beat Spezia 2-1. Sassuolo and Genoa drew 1-1.