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.
Cluj were the stronger of the two sides in the opening exchanges after Rui Pedro found himself in space in the Inter 18-yard-box following a good dummy by Gabriel Muresan, but the 24-year-old fired tamely past Samir Handanovic's far post.
Inter looked uncomfortable in the opening 10 minutes, but could easily have wrapped up the tie with their 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.
At the other end, Robert Maah did well to shuffle the ball onto his right foot, yet could not guide his curling effort on target having got the better of Andrea Ranocchia on the left side of the Inter area.
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 defence, before squaring to Guarin to tap into an empty net.
The Nerazzurri came close to doubling their advantage with 10 minutes remaining of the first half after Cassano played through to Palacio. The Argentine fired across goal, but saw his effort well saved by Mario Felgueiras.
Cluj were not prepared to exit the competition without a fight though, as Laszlo Sepsi shot from close range after substitute Pantelis Kapetanos came within inches of connecting with Ivo Pinto's pull back.
But Inter wrapped up the encounter on the stroke of half time 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, before Hora struck the bar late on as the Nerazzurri set up a last 16 tie with Tottenham Hotspur.