Orsic struck a fine hat-trick after Marin Leovac's opener to bring a stylish end to a run of 11 consecutive defeats in the competition for the Croatian champions.
Often one of Serie A's most exciting teams last season as they famously secured a place in Europe's elite tournament for the first time, Atalanta produced next to nothing in attack and were exposed all too easily at the back in a humbling defeat.
Dani Olmo's brilliant run led to Leovac's opener, the full-back converting Petar Stojanovic's cross from the right from barely six yards out.
When you want in on the fun 🤣 pic.twitter.com/zpeX45A70d— Bleacher Report Live (@brlive) September 18, 2019
Atalanta's susceptibility at the back was punished again 31 minutes in, Orsic side-footing home a fine finish from the edge of the box after more good work from Olmo and Leovac.
Dinamo fans were in raptures before the break, Stojanovic providing another telling cross that was diverted back across goal by Arijan Ademi, giving Orsic the simple task of nodding the ball into the net.
There was something of an Atalanta response after the interval, with Mario Pasalic volleying wide from a good position, but the miss was about the best Gian Piero Gasperini's side could muster.
Orsic compounded their misery and made it a night to remember for Dinamo, slotting in his third goal in confident fashion after Kevin Theophile-Catherine's hopeful ball caught out the entire Atalanta back line.
Duvan Zapata at last had a couple of openings but Dominik Livakovic produced a brilliant one-handed save to deny the striker before he prodded wide when played clean through.
What does it mean? Dinamo steal march in race for second
With Manchester City expected to win Group C comfortably, Dinamo, Atalanta and Shakhtar Donetsk are effectively in a three-way battle for the other qualification spot.
Dinamo certainly look the most likely to take it if they can build on this performance. They were clinical going forward and resolute defensively against a team that scored 77 goals in the Italian top flight last season.
Awesome Orsic unstoppable
Atalanta could not cope with the movement of Dinamo's front three, particularly on the break. Orsic was the pick of the attack and his first goal in particular was an outstanding finish.
Not one Atalanta player turned in a positive performance, but Rafael Toloi was especially weak at the back, unable to control Olmo and caught out of position for the fourth goal.
Dinamo, who face Varazdin in the league on Saturday, travel to Manchester City in their second group game, when Atalanta host Shakhtar.