Having lost all four of their previous league phase matches, Crvena zvezda knew a fast start was needed against their German visitors.
However, it was Sebastian Hoenel’s side who came flying out the blocks with a breakthrough inside five minutes, as Enzo Millot’s header inside the box was clinically fired home by Ermedin Demirovic.
Undeterred, the hosts found a swift response just seven minutes later when Silas dispossessed Millot in midfield before advancing to the edge of the box and curling a superb strike into the bottom corner.
The end-to-end nature of the contest continued as the first half progressed, and after Demirovic saw a goal ruled out for offside, Crvena zvezda completed their turnaround on the half-hour mark.
Seol Young-woo’s dangerous delivery into the box made its way through to Rade Krunic, who took one touch to compose himself before powering a finish into the roof of the net.
Determined to reassert their authority on proceedings, Stuttgart upped the ante at the start of the second half, seeing plenty of the ball in the final third.
Crvena zvezda remained a threat at the other end though, and could have extended their lead further when Silas and Cherif Ndiaye missed a couple of glorious chances before the hour mark.
Undeterred, Milojevic’s men continued to look dangerous and a third goal duly arrived in the 65th minute, with substitute Mirko Ivanic heading home at the back post from Timi Elsnik’s inviting corner.
Armed with all the momentum, the hosts sealed their victory with a fourth shortly afterwards, as Nemanja Radonjic applied the finishing touch to a brilliant counter-attacking move.
That goal effectively ended the match as a contest and Radonjic added his second of the evening late on with a clinical low strike as the hosts earned just a second win from their last 15 post-qualifying round matches in the Champions League.
Stuttgart, meanwhile, will be desperate to bounce back against Young Boys on matchday six after a second consecutive defeat in the competition.
Flashscore Man of the Match: Silas (Red Star Belgrade)