The Colombian netted a first-half brace to condemn the Romanian side to a Europa League exit at the last 32 stage.
The Colombian was left with the simplest of finishes after some good work by Ricky Alvarez and Rodrigo Palacio on the right flank, before tapping into an empty net following some poor goalkeeping by Mario Felgueiras to give the Italian side a 5-0 aggregate win.
The hosts ended the encounter with 10 men following Camora's dismissal with 10 minutes to go before Marco Benassi added a third in the final minutes of the tie.
Inter looked uncomfortable in the opening 10 minutes, but could easily have wrapped up the tie with its first attack of the game after Esteban Cambiasso played a probing ball through the Cluj backline, only for Antonio Cassano to blast over from 12 yards.
However, the tie was all but wrapped up in the 20th minute following some good work by Alvarez in his own half. The Argentine played through to compatriot Palacio, who was onside despite the best efforts of the Cluj defense, before squaring to Guarin to tap into an empty net.
Inter wrapped up the encounter on the stroke of halftime following some poor goalkeeping by Felgueiras after a heavy touch by Guarin. The ball found its way to Alvarez, who squared to the Colombian to side-foot into an open net.
A tepid second half finally kicked into life on the hour mark after Pinto broke well down the right. He pulled across goal for Pedro, only to see his side-footed effort blocked by Cambiasso and loop over the bar for a Cluj corner.
Ioan Hora then forced a superb point-blank range save from Handanovic after Inter failed to clear a free kick. The substitute beat the offside trap, but smashed his effort straight at the Nerazzurri number one on the 70 minute mark before Alvaro Pereira was forced to make a last gasp block to deny the same player minutes later.
The hosts continued to pepper the Inter goal as Camora forced a good save out of Handanovic before the same player saw red with 10 minutes to go having fouled Benassi.
Benassi then added Inter's third of the evening in the dying embers of the encounter after latching onto a long Cassano pass before tapping under Felgueiras to make it 3-0 on the night and 5-0 on aggregate. After advancing, the Nerazzurri set up a last 16 tie with Tottenham Hotspur.