Late Inter double gives Ranieri winning debut
Diego Milito won and converted an 81st-minute penalty and Lucio headed in from Sulley Muntari's free-kick in the 87th to give Inter their first win in six competitive outings this season.
Despite missing injured playmaker Wesley Sneijder, the 2009/10 treble winners went ahead through Giampaolo Pazzini just before half-time before Alessandro Diamanti levelled for Bologna with a penalty in the 66th minute.
"It was important to get off on the right foot, the lads needed to recapture their self-belief," former Valencia, Chelsea, Juventus and AS Roma coach Ranieri told the club's website (www.inter.it).
"I said it wasn't important whether we played well or badly but to get the result. The boys showed they are hungry... we showed the right spirit.
"Inter's standards are very high," added Ranieri. "We will score a few points, move towards the top of the table and then we will come out and fight with everything we have."
Ranieri became Inter's fourth coach since the departure of Jose Mourinho in May 2010 when he was named on Thursday to replace Gian Piero Gasperini, fired after only five matches.
Dutchman Clarence Seedorf, 35, curled in the only goal after five minutes to give injury-weakened Milan a 1-0 home win over Cesena who are bottom after losing all four games.
Milan, who did just enough to win, have five points from four games.
Napoli and Fiorentina drew 0-0 in Saturday's other game.
Fiorentina dominated the first half and were denied a goal when Morgan de Sanctis made a memorable point-blank save to turn away Cesare Natali's header. The game could have gone either way in an end-to-end second half.
Diego Forlan hit the post for Inter and Philippe Coutinho also went close as Ranieri's new team looked much more confident than they did in Wednesday's 3-1 defeat at Novara.
After a let-off when Marco Di Vaio broke clear for Bologna and side-footed over, Pazzini put the visitors ahead in the 39th minute with a low shot which slipped through Jean Francois Gillet's hands.
Second from bottom Bologna took control after the break, Diamanti converting a controversial penalty after pushing at a corner, and looked likely to score again until Milito was knocked over by Archimede Morleo in the area.
Morleo was sent off and Milito, left out of Argentina's squad on Thursday along with Inter team mates Esteban Cambiasso and Javier Zanetti, converted.
Lucio's near-post header made sure of the win to leave Inter with four points from four games.