The two sides played out an enthralling 3-3 draw in the first leg at Parkhead last week and, although Thursday's fixture at San Siro lacked that goalmouth action, the two sides still produced an entertaining affair.
Celtic saw defender Virgil van Dijk dismissed for receiving two cautions in the first half - the first of which seemed somewhat harsh.
From that point on, Inter were well on top and only some last-ditch defending and a fine goalkeeping display from Craig Gordon kept the scores level until Guarin produced something special in the 88th minute.
The Colombian picked up a pass from Davide Santon and arrowed a shot into the top corner from just outside the area.
The win extends Inter's unbeaten home run in the competition to 11 matches, stretching back to August 2012, while Celtic's focus will now return to clinching a domestic treble.
Celtic had the first genuine chance in the seventh minute when Gary Mackay-Steven bore down on goal, but goalkeeper Juan Pablo Carrizo spread himself well to smother the shot.
The visitors thought they should have had a penalty seven minutes later when Armstrong went down under a challenge from Santon, but Kruzliak waved away their protests.
Inter responded strongly and almost took the lead in the 19th minute when Santon's shot was just out of reach of a sliding Mauro Icardi.
Celtic were then dealt a major blow nine minutes prior to the interval as Van Dijk - perhaps harshly booked for an earlier foul on Rodrigo Palacio - was shown a second yellow for pulling back Icardi.
Seemingly buoyed by their man advantage, Inter twice went close to moving ahead when Xherdan Shaqiri was kept out by a fine block from Jason Denayer, before Gordon saved smartly with his legs from Danilo D'Ambrosio's rebound.
Palacio ought to have put the hosts ahead four minutes into the second half, but blazed over after a clever pass from Guarin.
Gordon pulled off a fine save low to his left to keep out Hernanes four minutes later, before the goalkeeper produced an even better stop to deny Icardi soon afterwards.
Substitute Kris Commons brought a comfortable save out of Carrizo with a speculative 40-yard strike eight minutes from time, but it was a rare effort on goal as Celtic tired.
With two minutes remaining, Guarin picked up the ball 25 yards from goal and thumped an unstoppable shot beyond Gordon into the top left-hand corner to seal Inter's passage.
