Clarence Seedorf's side could consider themselves in the vital sixth spot for just six precious second-half minutes on Sunday as Parma's win at home to Livorno proved enough for Roberto Donadoni's men.
Last season, Milan snuck into the UEFA Champions League on the last day at Fiorentina's expense, but there was to be no repeat.
The game is widely expected to be Seedorf's last in charge of Milan - despite promising bursts of form the Dutchman has ultimately been unable to inspire the club to a sufficient charge up the league.
Sassuolo came into the game having secured their survival last week and were aiming to do a domestic double after ending Massimiliano Allegri's reign with a stunning 4-3 win in January.
But Sulley Muntari settled any home nerves with a second-minute thunderbolt and Nigel de Jong doubled the advantage before the half hour with a deflected free-kick.
Philippe Mexes was dismissed for two bookings and Sassuolo - who were also reduced to 10 men late on when Paolo Cannavaro saw red - may find themselves having ultimately accounted for two Milan coaches in their debut Serie A campaign.
Simone Zaza scored a penalty in stoppage time to end Sassuolo's fine season on a high, Mattia De Sciglio seeing red for the foul.
Milan made a superb start as Muntari fired in a swerving left-foot effort from 25 yards that pinged into the net off Alberto Pomini's right-hand post.
Lorenzo Ariaudo spurned a great chance to equalise as he turned over from eight yards, but the hosts were in the ascendancy with Pazzini and Kaka both forcing Pomini into fine diving saves.
Pazzini saw a goal rightly chalked off for offside before Milan did double their advantage soon after as De Jong's set-piece came off Zaza in the wall and wrong-footed the goalkeeper.
De Jong made a point to celebrate with the under-fire Seedorf, who has often found public backing from the Milan board hard to come by.
Zaza found himself clear on goal 10 minutes into the second period, but Adil Rami stormed back to make a fine block.
And the visitors looked inspired with Domenico Berardi's effort tipped over by Christian Abbiati, who also saved Cannavaro's header from the resulting corner.
Substitute Stephan El Shaarawy drew a save from Pomini in his first act after emerging from the bench.
But Milan's attacking threat was stifled when Mexes was sent off for picking up a second yellow card with 20 minutes to go, with Cannavaro following him down the tunnel 20 minutes later for clattering El Shaarawy.
Referee Paolo Valeri was in the spotlight most in the closing stages, flourishing his third red card in De Sciglio's direction for fouling Nicola Sansone in the penalty area.
Zaza stepped up to force home the spot-kick, ending Milan's desperate season on a sour note.
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