Walter Mazzarri's men had gone three games in a row without a win but the Argentine's first-half spot kick ensured they picked up the victory over their 10-man hosts
The build-up to Sunday's clash had been dominated by headlines surrounding honorary president Massimo Moratti's resignation from his post - reportedly having lost faith in the former Napoli tactician - but a narrow victory over 17th-placed Cesena should see Mazzarri continue to cling on to his job.
Inter's poor start to the campaign saw them go into the weekend in ninth place, and they were given a helping hand when the hosts' goalkeeper, Nicola Leali, was controversially sent off for a coming-together with Rodrigo Palacio.
Mauro Icardi scored from the resulting penalty to give Inter the lead and although the visitors failed to add to that advantage - Hugo Campagnaro seeing a late second disallowed for offside - they had more than enough to claim all three points.
Mazzarri had declared an "emergency situation" after the events of Thursday, which saw Moratti's resignation followed by a 0-0 draw with Saint-Etienne in the Europa League.
But although they initially struggled to create clear-cut chances, they eventually began to control the tempo.
There was an element of good fortune about their 32nd-minute opener, though.
Palacio raced on to Hernanes' delightful chipped pass and theatrically fell to ground in expectation of a collision with Leali, earning the goalkeeper a red card before Icardi converted the resulting penalty.
Cesena went close to restoring parity twice in the following three minutes, as Emmanuel Cascione first blazed a half-volley over from around 10 yards, before Samir Handanovic acrobatically palmed away Milan Djuric’s header.
Palacio thought he had made Cesena pay just before the break as he beat Federico Agliardi – Leali's replacement – from a tight angle, only for his celebrations to be cut short by the offside flag.
Inter continued to see more of the ball at the start of the second half, but again Cesena should have drawn level in the 54th minute as an unmarked Guido Marilungo headed over from eight yards.
The visitors finally began to click as attacking force after that let-off - Hernanes firing agonisingly wide after a solo run in the 58th minute, before Mateo Kovacic saw his 20-yard effort just miss the target.
They could have made the result more comfortable in the latter stages, as Palacio shot straight at Agliardi when through on goal and then Campagnaro saw his 85th-minute header disallowed for offside.
But Icardi's penalty proved to be enough as Mazzarri's men came away from Stadio Dino Manuzzi with all three points.