Rodrigo Palacio was on target twice for the Italian side but their talismanic Argentine attacker faces a lengthy spell on the sidelines after suffering serious ligament damage
Two goals either side of half-time from Rodrigo Palacio helped Andrea Strammacioni's side to their second win in as many games in all competitions, with recent young signing Mateo Kovacic gaining his first team debut.
Despite being the visitors, Cluj started positively, and in the fourth minute Robert Maah fired a sweetly-caught half volley towards goal, which curled wide of Samir Handanovic's post. Moments later, Inter faced an early injury setback, as Diego Milito lay in agony following an awkward fall.
Inter started sluggishly but almost took the lead in the 16th minute. After breaking quickly, Antonio Cassano carried the ball infield before looping a well-weighted cross to the back post in search of Esteban Cambiasso. The Argentine controlled the ball well, but was seemingly hesitant to shoot from a good position with Felgueiras standing tall, as his lame attempt at a cross flew harmlessly out of play.
Four minutes later, frustration within the stadium turned to joy, as substitute Palacio raced through on goal following a Fredy Guarin pass, before calmly lofting the ball over the Cluj goalkeeper and into the net. The Argentine's goal was a result of an unforced Cluj error, as the Romanian side generally fared better in a tentative first half.
The hosts' fortunate lead was almost cancelled out on 22 minutes, however, as Cluj should have levelled from a Laszlo Sepsi cross. The pacey delivery from the left skidded across Inter's six yard box, with Rui Pedro unable to get a finishing touch.
On 36 minutes, Palacio was slipped through on goal once again, but this time Felgueiras raced out quickly and made himself big to deny the goalscorer. Seconds later, Cassano similarly got in behind the Cluj defence, but Ricardo Cadu recovered well to deny the him a shot on goal.
Deep into first-half stoppage time, however, Handanovic was called into action for the hosts, diving low to his right to palm away a Rui Pedro free-kick.
Both sides began slowly in the second half, with Cluj continuing to shade possession but creating limited chances. Goals seemed to be dependant on individual mistakes, with only Cassano and Guarin for Inter visibly possessing the tools to unlock the opposition defence.
Inter's first significant chance came on 62 minutes, when Cassano was presented with the chance to double his side's lead, as a deep cross was directed in his direction by a Guarin header. The 30-year-old was set to lash the ball past the helpless Cluj keeper from seven yards, but failed to get any true contact on the ball.
Palacio raced through after receiving the ball down the channel in the next attack, but he saw his effort rebound off a defender and to safety.
A sloppy midfield battle ensued in the latter stages, as both sides struggled to enjoy a decent spell of possession. Cluj dropped deeper, seemingly happy with a one-goal deficit, allowing Inter to have more of the ball in advanced positions.
After the substition of Cassano for Ricky Alvarez in the 73rd minute, Inter lacked the quality to trouble the Cluj defence, who stood resilient in their path.
The best chance of the second half for the visitors came in the 83rd minute, as the ball was worked out to the left flank to Sepsi, following a mistake from the home side. The Romanian could not find a team-mate with his centred ball however, as his cross looped out of the 18-yard box.
Three minutes later, Inter doubled their lead, courtesy of the same man who grabbed their opener, Rodrigo Palacio. The Argentine raced through on goal after a defence splitting through ball and chipped Felgueiras with a delightful lob, to seal a solid home win for his side.
Despite not playing their best, Inter will go to Romania with a two-goal cushion, and Stramaccioni will feel that if Nerazzurri can grab an early away goal in Cluj, the tie may well be theirs.