Seven-time European champions Milan have failed to hit the heights for the past few seasons and owner Silvio Berlusconi said last week he is ready to sell the club to "the right buyer, preferably an Italian".
In the meantime, the Rossoneri are battling to beat Sassuolo to finish in sixth place -- which will be bestowed a Europa League spot if champions Juventus beat Milan in the Italian Cup final.
Bologna have secured top flight football for next season under Roberto Donadoni, who was parachuted in last October as the club plummeted under the guidance of Delio Rossi.
Having been cautioned for an altercation with Jose Mauri, Diawara was given his marching orders after ploughing through Milan captain Riccardo Montolivo minutes later.
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Yet in a scrappy game of few real chances yesterday, it took Bacca's 40th minute spot-kick -- after goalkeeper Angelo Da Costa hauled down Luiz Adriano in the area -- to seal the points.
Milan moved up one place to sixth, two points ahead of Sassuolo before they visit relegation-haunted Frosinone on Sunday.
The Argentine hobbled off just after the hour on Saturday with a knock that is expected to sideline him for next week's trip to Sassuolo, a match keeper Samir Handanovic and winger Ivan Perisic will miss through suspensions after picking up late bookings for time-wasting.
Inter coach Roberto Mancini, meanwhile, admitted their absence from Europe's top table next season weighs heavily.
"It's weighing on everyone the fact we won't be playing in it," said Mancini, who won seven trophies including three consecutive league titles in his previous spell at the club in 2004-2008.
Inter had the perfect start, Icardi firing first-time into the roof of the net on 12 minutes from Perisic's smart pull-back.
Empoli reduced the arrears eight minutes before the interval thanks to Manuel Pucciarelli, but just three minutes later Perisic tapped home the rebound after keeper Alberto Pelagotti spilled Stevan Jovetic's shot.
In the end Inter were thankful for the points after Pucciarelli was ruled offside after drilling into the roof of the net and Andrea Costa saw a bouncing volley go just wide of Handanovic's post.
Today champions Juventus are away to relegated Verona in what will be home striker Luca Toni's final fixture after 22 years as a professional.
Roma win at home to Chievo in today's early game would send Luciano Spalletti's men up to provisional second place with a one-point lead on fellow Champions League qualification rivals Napoli, who travel to Torino later in the day.