The Serie A leaders had to settle for a disappointing 1-1 draw against Atalanta in the league on Saturday with Conte's injury-hit squad lucky to hold on for a point after conceding a late penalty which was saved.
Atalanta had a golden chance to snatch all three points from the penalty spot with two minutes of regulation time remaining, but Handanovic dived to save Luis Muriel's spot kick.
Milan's victory places them in 10th place with 25 points.
Elsewhere, Udinese beat Sassuolo 3-0, Fiorentina were 1-0 winners at home to SPAL, Sampdoria thrashed Brescia 5-1, Genoa lost 2-1 at Hellas Verona while Torino scrapped to a 1-0 victory over Bologna.
Sanchez was an unused substitute in the draw with Atalanta, as he was in the previous match as Inter won at Napoli.
Juventus have the opportunity to overtake Inter at the top of Serie A on Sunday night if they can pick up a win away at Roma, which would sour Conte's mood still further. Monaco, on the other hand, drops to 8th with 29 points.
Second-placed Marseille saw Kevin Strootman net the victor in the 84th minute as they beat Rennes 1-0 on Friday night.
Marseille will have the feeling of being back in the running for the title with 41 points despite one more game than PSG.
Maxwell Cornet and Moussa Dembele scored for Lyon, who were behind Jimmy Briand in the first period.
"Looking at the table, seeing us up there, we might turn a blind eye to some issues, but the fact remains I pray we don't have any players missing, otherwise there's no cover", Conte told DAZN. Before Julio Tavares marked what turned out to be the victor at the end, Hamza Mendyl was shown a straight red and later Boubakary Soumare received his order for two reservations.