Inter won 2-1 at relegation-threatened Genoa to move a point ahead of Milan and two points above Napoli, who lost 1-0 at Udinese on Sunday.
At the San Siro, Ismael Kone gave Sassuolo a surprise 13th-minute lead but the hosts levelled in the 34th as Ruben Loftus-Cheek rolled the ball across the area for Bartesaghi to power in from close range.
The 19-year-old Bartesaghi doubled his tally immediately after halftime when he ran onto Christopher Nkunku's smart pass and fired inside the near post.
Christian Pulisic and Loftus-Cheek both had goals disallowed for Milan before Sassuolo equalised in the 77th minute through substitute Armand Lauriente.
Napoli knew they could go top following Milan's result.
However, it was Udinese that had the better of the chances and twice thought they had opened the scoring only to have both goals struck off on video review.
The home side finally broke the deadlock in the 73rd minute when Jurgen Ekkelenkamp curled a magnificent strike into the far top corner from outside the area.
Instead it was Inter who moved into the sole lead of Serie A with what looked set to be a routine win, until the final 25 minutes.
Yann Bisseck got Inter off to a perfect start with an early goal and Lautaro Martinez doubled his side's advantage shortly before halftime.
Vitinha pulled one back for Genoa midway through the second half after squeezing his way through two defenders and rounding Inter goalkeeper Yann Sommer.
Elsewhere, Juventus won 1-0 at 10-man Bologna to leapfrog their opponents into fifth place — one point below the top four.
Substitute Juan Cabal headed Juve in front in the 64th, three minutes after coming off the bench.
In Florence, Gift Orban scored twice — including in added time — as Hellas Verona won 2-1 over last-placed Fiorentina in a relegation battle to move to within two points of safety.
Fiore are without a win and eight points from safety after 15 rounds. Their fans displayed a banner addressing their Verona counterparts with the words "whoever finishes last pays for the drinks."
