On Thursday, Inter were knocked out of the Coppa Italia by Lazio on penalties, a result that followed a defeat by Torino and draw with Sassuolo in their first two league games since the winter break.
The visitors sacked Filippo Inzaghi following a 4-0 defeat to 19th-placed Frosinone last week after a run of one win in 16 games, replacing him with former Inter player Mihajlovic.
The Serbian enjoyed a dream start to his second spell in charge of Bologna, having previously led them during the 2008-09 season, as Santander’s first-half header earned the Rossoblu three points that move them to within one point of the safety zone.
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Mauro Icardi squandered a great chance for Inter early on, shooting wide while unmarked eight yards from goal, before Samir Handanovic was on hand to deny efforts from Riccardo Orsolini and Santander.
The goal arrived when the Paraguayan striker nodded in from a corner at the front post and Inter, who have yet to score in three league games this year, struggled in the final third again.
Lautaro Martinez headed wide from a good position and makeshift striker Andrea Ranocchia’s volley forced a smart save from Lukasz Skorupski.
Inter remain in third on 40 points, but have fallen 11 points adrift of second-placed Napoli.