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Nainggolan, having cemented his starting place with the Red Devils with his match-winner against Sweden in the final group stage game, helped his side cruise past Hungary - with Toby Alderweireld, Michy Batshuayi, Eden Hazard and Yannick Ferreira Carrasco scoring the goals.
Afterwards Nainggolan - who provided the assist for Ferreira Carrasco's injury-time clincher - took to Instagram to celebrate the result.
"Great victory," Nainggolan wrote on Instagram. "Let's continue like this!"
Belgium will now place Wales in the last-eight, with the game scheduled for 2100 CEST on Friday 1 July.
There was not the same celebration for Gyomber, however, despite the 23-year-old being named in Slovakia's starting lineup for the first time in the tournament.
Jan Kozak's side put up a determined defence against Germany but were eventually overwhelmed, with goals from Jerome Boateng, Mario Gomez and Julian Draxler securing a 3-0 win.
Three more Roma players could be in action on Monday, as Italy face Spain in Paris. Daniele De Rossi, Alessandro Florenzi and Stephan El Shaarawy are all vying for a place in Antonio Conte's starting lineup.
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