The Italian side eased the pressure on under-fire coach Andrea Stramaccioni, whose position had come under increased scrutiny after a 4-1 defeat to Fiorentina on Sunday had left them with just one win in five Serie A games.
But Guarin netted twice and Marco Benassi scored a late third as Cluj were forced to play the final 10 minutes with 10 men following the sending off of Mario Camora in the second leg of their last 32 Europa League fixture.
The first leg had seen Inter lose Diego Milito to a season-ending injury but they did not miss the Argentinian striker in Romania.
The home side carved out the first opening in the fifth minute but Rui Pedro shot wide left of the goal.
But with nine minutes gone Cluj were forced into a change when the injured Gabriel Muresan was replaced by Ioan Hora.
Antonio Cassano hit a shot over the bar as Inter came more into the game.
Cluj's Roberto Maah was off target as the home side continued to look for a way back into the tie.
The game became a battle of the midfield with both teams winning free-kicks but unable to turn possession into chances.
Inter went further ahead in the tie when Guarin opened the scoring on the night with a finish from close range after Rodrigo Palacio had set up the chance in the 22nd minute.
Palacio had a shot saved by Cluj goalkeeper Jorge Mario Felgueiras as Inter attempted to press home their advantage.
Inter keeper Samir Handanovic was forced into his first save as half-time approached as he blocked an effort from Hora.
Laszlo Sepsi then shot wide as Cluj tried to put Handanovic's goal under more pressure.
Guarin netted his second in first half injury time with a shot from close range from a pass by Ricardo Alvarez.
Inter were forced into a change at the break with the injured Palacio replaced by Benassi.
Cluj's Rui Pedro tried his luck from distance but shot over from the edge of the area.
Sepsi drilled a free-kick into the wall before Hora went close for Cluj when his shot from close range was kept out by a fine Handanovic save.
Guilherme Juan blocked a shot by Pantelis Kapetanos and then Hora's effort was kept out by Alvaro Pereira as Cluj tried to find a way through.
Handanovic pulled off another fine save as Camora saw his shot kept out.
With 10 minutes to go Cluj were reduced to 10 men when Camora was sent off for a professional foul on Benassi.
Handanovic kept out another shot by Kapetanos as the home side again failed to find a way through the Inter defences.
The Italian side wrapped up the tie and a last 16 meeting with Tottenham when Benassi netted with two minutes to go.
There was still time for Hora to hit the bar with a shot in a failed bid for a late consolation goal.