His first-half goal put Gian Piero Gasperini's men in front and despite an equaliser from Marco Sau early in the second half, the visitors soon pulled away.
Atalanta scored again through Rafael Toloi, Duvan Zapata and Luis Muriel to remain in contention near the top of the table.
Zapata and Toloi both earned impressive 7.8 FC Ratings but no one came close to the masterful Ilicic.
Josip Ilicic: Best stats
Ilicic ended the match with a goal as well as an assist for Zapata's strike but that is only telling part of the story.
To achieve a perfect 10 you also have to excel in so many other areas, which the 32-year-old did.
He created four big chances in the match, completed 10 dribbles and had eight crosses - all of which were game highs.
Ilicic was a constant threat, racking up six shots and having 12 touches in the opposition box, again figures which no one else on the pitch could rival.
He had 39 passes in the final third of the pitch, well clear of the second best performer in that category, team-mate Remo Freuler (22), while he also had 92 touches, the most in the match.
It was not just on the ball Ilicic impressed. He also won 14 of his 16 duels in a memorable 87-minute outing.
His season so far
The only performance that comes close to this in Ilicic's 2020/21 season so far was when he achieved an 8.9 FC Rating after getting a goal and two assists in the famous 4-1 win over Roma last month.
He averages an impressive 7.3 in 10 Serie A games this season, making him our sixth-highest rated player in Italy's top flight from those who have played at least 500 minutes.
The players above him make up a pretty impressive list: Zlatan Ibrahimovic, Cristiano Ronaldo, Henrikh Mkhitaryan, Lorenzo Insigne and Manuel Locatelli.