Samuel Eto'o fired home a second half goal to give Inter a 1-0 second leg win at Fiorentina to make sure they stayed in the hunt for the Cup, Serie A and Champions League trophies.
"We played the match we had to play. It was perfect," Inter assistant coach Daniele Bernazzani told Rai television with manager Jose Mourinho continuing his media boycott for domestic games.
"It's a delicate moment because fortunately we have everything to play for. I'd pay to be in this situation at this stage every year, in the running in all the competitions."
Mourinho had taken the rare step of leaving several first-choice players out of his starting XI ahead of Friday's Serie A clash with Juventus and next week's Champions League semi-final first leg against Barcelona.
The Italian champions were facing Fiorentina for the second time in three days after being held to a 2-2 draw on Saturday in the league, a result which allowed AS Roma to snatch top spot in Serie A.
On Tuesday, Inter created several chances early on with Mario Balotelli hitting wide from a good position after pinching possession.
However, they also wobbled at the back, with Lucio clearing off the line and Cristian Chivu conjuring a desperate challenge to deny Fiorentina forward Alberto Gilardino.
The visitors subdued the tempo in the second half after delaying the restart by around five minutes by emerging from their locker room late.
Balotelli forced a finger-tip save from Sebastien Frey with a 30-metre strike before Cameroon forward Eto'o sprinted on to Thiago Motta's pass to spring the hosts' offside trap.
He controlled the ball and slammed it home in the 57th minute.
Eto'o's goal effectively ended the contest, leaving Fiorentina needing to score three times to go through.
"We conceded a goal and then we lost faith," Fiorentina boss Cesare Prandelli said. "We risked an offside trap that we shouldn't have and we were punished."
Inter will meet the winner of the other semi between Roma and Udinese, with the Romans carrying a 2-0 lead to next week's second leg.
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