The Brazilian midfielder converted from the penalty spot before wrapping up proceedings late in the piece to finish off Chelsea's pre-season tour of the US in style.
The opening goal for Conte's side came on 24 minutes when Bertrand Taore poked home from inside the area after Victor Moses' initial shot being saved.
Brazilian midfielder Oscar only entered the fray in the 58th minute when replacing Cesc Fabregas and within 10 minutes, was side-footing beyond Gianluigi Donnarumma from 12 yards after Eden Hazard's intended cross had been handled by Andrea Poli.
The fourth and final goal of the contest occurred in the 87th minute when second-half sub Juan Cuadrado attracted a pair of Milan defenders down the right before supplying Oscar with a lovely ball which the Brazilian dully smashed home.
The match was played in front of 64,101 supporters - a record for football in Minnesota - and caps off a solid Stateside tour for both teams.
Chelsea will next meet German club Werder Bremen on Sunday after flying back to London on Thursday, ahead of their Premier League season opener against West Ham United on August 15, while Milan take on SC Freiburg in Germany next weekend prior to their Serie A kick-off against Torino on August 21.