"That's how you dream of your debut going," said Gregoritsch as the Bundesliga returned after a four-week winter break.
"The fact that it worked so well is great and something very special for me."
Gregoritsch, who joined last month on loan from Augsburg until the end of the season, shone up front as Schalke moved up to fourth place, level on 33 points with third-placed Bayern Munich, who they play away next weekend.
Like Bayern, Schalke are now four points behind league leaders RB Leipzig, who host mid-table Union Berlin on Saturday.
"We weren't good enough to cause Schalke trouble," admitted Moenchengladbach captain and goalkeeper Yann Sommer.
"We didn't find the room and weren't fast enough. Schalke were clearly better. They put a lot of pressure on us."
Schalke earned a goalless draw in Moenchengladbach when the teams met in August, but the Royal Blues dominated at the Veltins Arena in front of 62,251 fans on Friday.
They took control after the break when Gregoritsch drew a couple of defenders wide on the left and spotted midfielder Suat Serdar unmarked in the middle.
The Germany midfielder was well outside the box but took his time to curl a brilliant shot past Sommer on 48 minutes.
Austria international Gregoritsch then grabbed a goal of his own when Schalke countered at pace after a Gladbach attack broke down.
Central midfielder Daniel Caligiuri put Belgian striker Benito Raman away into space on the left and he spotted Gregoritsch charging into the box, with the debutant sweeping home a second on 58 minutes.
The defeat kept Gladbach second in the table, but they can be leapfrogged by Bayern who visit mid-table Hertha Berlin on Sunday.