The three-times Olympian surprisingly failed to make the podium in the women's 800m freestyle before roaring back to win both the 200m and 200m individual medley at the Olympiisky Swimming Pool.
American juniors Leah Smith and Becca Mann were able to take advantage of Hosszu's early lethargy, taking gold and silver respectively in the 800, with Russia's Elizaveta Gorshkova coming in third.
In the 200m free, Hosszu edged compatriot Zsuzsanna Jakabos for the win, while China's Guo Jinjin came third.
That one-two was repeated in the 200 IM, with Great Britain's Sophie Allen finishing in the bronze medal position.
Hosszu completed a satisfactory night by picking up her third podium in the 200m backstroke, finishing third behind New Zealand’s Melissa Ingram and Kylie Stewart of the US.
In the 100m breaststroke, America's Jessica Hardy was disqualified in the preliminaries for not separating her hands prior to a dolphin kick, allowing Rie Kaneto of Japan to go on an claim gold ahead of team-mate Mio Motegi.
Italy’s Ilaria Bianchi won the 100m butterfly, while Rachel Goh of Australia took gold in the 50m backstroke and Germany’s Britta Steffen won the 50m freestyle.
On the men's side, Laszlo Cseh was unable to stop Japanese teenager Daiya Seto winning the 400m IM, the Hungarian having to make do with second ahead of Israel’s Gal Nevo.
Seto went on to grab another podium later in the evening: silver in the 200m fly behind compatriot Kazuya Kaneda.
Paul Biedermann won the 400m free - albeit in a time 11 seconds slower than his own world record - while Tommasso D’Orsogna of Australia claimed victory in the 100m free.
Italy’s Fabio Scozzoli took his first win of the series in the 50m breast while Stanislav Donets of Russia delighted the home crowd with victory in the 100m back.
And there were victories for American Sean Mahoney in the 200m breast, Kenneth To of Australia in the 100m IM and Matt Targett in the 50m fly.
Rounding off the first night of action, the American mixed 200m medley relay team tasted victory, ahead of Russia and a Russian B team, in an unofficial world record.
The FINA World Cup is a global circuit of two-day meets with cash prizes on offer for individual races.
Moscow is the fourth of eight stops on the tour, with Hosszu currently topping the overall earnings for the women and To for the men.
Last year, Chad Le Clos and Therese Alshammar banked six-figure sums from the events.