The result left Red Star second in the 16-team league, four points behind champions Partizan Belgrade who stayed in the driving seat after captain Sasa Ilic converted a second-minute penalty to give them a laboured 1-0 win a Javor Ivanjica.
Milijas, who scored nine goals in 73 appearances for Wolves from 2009-2012, won praise from Red Star's coach Ricardo Sa Pinto who chalked up his fourth straight win since taking over last month.
"The lad can play for top clubs in Italy or Spain in the future if he carries on like this," Sa Pinto told reporters after the 29-year old playmaker headed the opener and scored another two after Spartak equalised in the cauldron of Red Star' stadium.
"I am happy with the overall performance and (striker) Darko Lazovic should always be playing at the level he demonstrated in the second half," added the former Sporting Lisbon and Portugal forward.
The home fans lit dozens of flares after Milijas restored Red Star's lead with a penalty and scrambled home the fourth from close range thanks to good work by the talented Lazovic, who made it 3-1 with a cool finish several minutes earlier.
Partizan ended a three-game winless streak, during which they saw their advantage at the top slashed by seven points, after Ilic drove in the spot kick following a rash tackle on midfielder Darko Brasanac.
I didn't scorn the players when they collected only two points from the previous three games so I am certainly not going to do it now because the win is all that matters," Partizan coach Vladimir Vermezovic said after a tepid performance.