A late goal proved enough for the north London outfit to join fellow English sides Chelsea, Tottenham and Aston Villa in the last eight after overcoming last season’s winners
The Gunners named a strong side which included Serge Gnabry, who made his Premier League debut earlier in the season at Norwich, and former Barcelona youngster Hector Bellerin.
The match at the Centro Sportivo Facchetti in Lombardy started evenly with both sides enjoying spells of possession.
It was the Italian outfit who had the first opportunity to break the deadlock in the 15th minute, but Lorenzo Lassi failed to force Deyan Iliev into action with a long range effort.
Inter continued to push for an opening but were thwarted by a string of excellent pieces of defending by a number of Arsenal players - with Elton Monteiro in particular shining.
However, despite dominating the latter stages of the half, the Italian side failed to create any real chances and the game headed into the interval goalless.
The rain continued to fall as the second half begun, making it hard for either side to get their passing styles going, with Arsenal resorting to trying to test Raffaele Di Gennaro with a number of long ball in to his area.
One of the stand-out players of the match was Chuba Akpom, whose pace and trickery looked like troubling Inter’s backline whenever he picked up the ball.
The deadlock was finally broken in the 68th minute when Yennaris picked up the ball near the halfway line before pushing forward and unleashing a strike past Di Gennaro from 30 yards out.
Inter came close to levelling the match with 10 minutes to play when Monteiro came close to putting the ball in his own net after intercepting Andrea Bandini’s cross.
Bandini whipped in another cross a minute later which Tassi did well to get up and meet but he could only head over.
The defending champions continued to push for an equaliser but failed to force to take the match into extra-time.
The result means Arsenal join fellow English sides Chelsea, Tottenham and Aston Villa in the last eight, where they will battle it out with CSKA Moscow for a semi-final berth.