The Gunners headed into the game knowing that they required a perfect record from their final two Group F outings, as well as a favour from elsewhere, which was duly provided by Bayern Munich beating Olympiacos in Bavaria.
Here, Sports Mole takes a look back at how the one-sided affair unfolded in North London.
On target: 7
On target: 1
Was the result fair?
The possession stats may suggest that this was an evenly-matched contest, but it was as comfortable as you like for an Arsenal side who retain strong hopes of keeping alive their proud record in this competition. Not since the turn of the new millennium have the Gunners failed to make it out of this initial group stage of Europe's showpiece competition, yet they faced the stark reality of crashing out at this early stage following a poor set of results thus far.
While it is worth remembering that the North London outfit did come up against a side boasting a weak record, they still had to remain focused on the task in hand which they sure enough did. It took Arsenal 29 minutes before they finally registered a shot on target, having dominated things up until that stage without having anything to show for their superiority.
Ozil's close-range header seemed to lift a weight off the players' shoulders, though, allowing the hosts to find their attacking groove which led to a further couple of strikes. It was not until the third goal hit the back of the net that Zagreb showed some of the capabilities witnessed in the opening round of fixtures when pulling off a stunning upset against Arsene Wenger's men, though a shock of a similar kind was never really on the cards this evening.
There had been a sense that the wheels were beginning to fall off Arsenal's campaign following a run of one win in their last five prior to tonight, with just a few questions once more being asked of experienced manager Wenger, but this was a positive response to Saturday's setback at West Bromwich Albion. It was not the greatest performance ever witnessed from the 2006 finalists, yet their key players - Sanchez and Ozil - stood up to the test when required.
Ozil, who perhaps should have added a third prior to the break when squandering two decent openings that Eduardo was equal to, has now been involved in nine of his side's last 12 goals, going some way to proving that his hefty price tag was indeed worth every last penny. Sanchez, too, continues to make a positive impression, himself being directly involved in seven of Arsenal's last nine Champions League goals.
A fair few supporters may have opted to stay away tonight - more on that a little later - but in terms of the action on the field not a lot more could be asked of the Gunners. The 17-year record of making it out of the group stage is now in sight, with Wenger knowing that he simply has to pick up a two-goal win in Athens next month to get the job done.
Dinamo Zagreb's performance
Since seeing their whopping 45-game unbeaten streak come to an end at the hands of Bayern Munich earlier in this year's competition, a run stretching back almost exactly a year, Dinamo have struggled to find any real momentum. It is now six defeats in 11 for the Croatian outfit in all competitions, with this performance arguably the weakest of the lot.
Zagreb appeared to be happy to sit back and hit their opponents on the break, which is not the worst tactic to deploy when playing away from home against one of European football's biggest forces. After going a goal down, thus making that plan essentially redundant with a win required, Zoran Mamic failed to properly set his side and Arsenal soon built up a head of steam.
Mamic's men had just the one shot on target, coming on the end of a deflected effort which forced Petr Cech into a sprawling save when the game was long over. It was not until the third goal of the night hit the back of the net that we finally saw the visitors show just a little attacking threat, but it was nowhere near enough to truly trouble their comfortable opponents. Defeat brings Zagreb's European participation to an end for another year, while the Gunners are now guaranteed a Europa League berth at the very least.
Sports Mole's man of the match
Alexis Sanchez: Ozil and Sanchez linked up throughout the match, including right at the death when the latter latched on to his teammate's scooped pass over the top and flicked the ball narrowly wide of goal. Sanchez just about edged things on the night in terms of personal performance due to his second goal, coming after Joel Campbell played a superb defence-splitting ball through to the Chilean attacker.
The Emirates Stadium attendance was announced as 58,978 this evening, but the official figure is surely much lower. This famous venue was nowhere near full capacity, as many supporters opted to stay away on this winter night following an abject run of results in the competition thus far from their side on the whole.
Not the busiest of games for Viktor Kassai, who had very little to do across the 90 minutes. Sanchez felt that he should have had a penalty in the second half, but his shouts were somewhat harshly waved away.
Arsenal: Wenger takes his group of players to Greece in a fortnight for that must-win showdown, but in the meantime Arsenal face strugglers Norwich City and Sunderland in the Premier League.
Dynamo Zagreb: The Blues will look to put tonight's disappointment behind them when they face feeder club Lokomotiv Zagreb at the weekend in the Croatian top flight.