The 21-year-old right winger set up the first goal after just 18 seconds with a sharp cross from the right, which striker Nikola Stojiljkovic turned in from seven metres, and then rifled in a crisp low volley in the closing stages to pile the pressure on Red Star coach Slavisa Stojanovic.
Red Star are now fifth in the 16-team first division on 13 points from eight games, four adrift of second-placed Cukaricki and leaders Partizan Belgrade, who were held to a 0-0 home draw by Javor Ivanjica on Saturday.
"All credit to our rivals because they wanted it more, showed heart and took their chances while we made schoolboy defensive errors and there is no doubt I will have a meeting with the board to see what's the best course of action," Stojanovic told a news conference.
"Whatever central defensive pair I field they keep making calamitous mistakes but that's the kind of quality, or lack of it, we have to make do with at the moment."
His counterpart Vladan Milojevic said: "We have a young team whose limits are still anyone's guess and we can afford to celebrate for a day ahead of the international break because we beat a club of great stature.
"Then it's back to hard work in order to keep up the momentum in an effort to stay up here as long as possible."
Srnic, who spent last season on loan at Cukaricki and completed a permanent move on a free transfer during the close-season, delighted the home fans early in the match by teeing up Stojiljkovic.
He ensured the win and silenced raucous Red Star fans with a superb finish which left visiting keeper Boban Bajkovic grasping at thin air.
Third-placed Vojvodina kept up the pressure on the pacesetters after Enver Alivodic and Nebojsa Kosovic helped them to a 2-1 win at Rad Belgrade, while Radnicki Nis climbed one place to fourth after a 1-1 home draw with Jagodina.