Belgrade's bitter foes have 59 points each, with Partizan leading the way on goal difference, while third-placed Vojvodina Novi Sad stayed only three points adrift after coming from behind in a 2-1 home success against struggling Hajduk Kula.
Ghana striker Prince Tagoe scored to send the champions on their way against Smederevo in their bid to capture a record fourth successive league title.
Midfielder Stefan Babovic made it 2-0 and Dragan Ceran pulled one back on the stroke of half-time before Ivica Iliev and Zvonimir Vukic sealed Partizan's win.
Red Star continued to look a much improved side under former Croatia midfielder Robert Prosinecki, who won the European Cup with the club in 1991.
South American flair in midfield set the tone on a warm evening as Colombian Cristian Borja and Brazilian Evandro lit up Red Star's seventh successive league win under Prosinecki with superb individual goals.
Striker Andrija Kaludjerovic continued his good run of form with a close-range header, teenage centre-back Uros Cosic scored his first goal for Red Star after a flowing team move and Darko Lazovic curled in a delightful shot from 25 metres.
Vojvodina, who are vying for their first league title since 1989 when Serbia was still part of communist Yugoslavia, looked in trouble after they fell behdind to an early Nemanja Boskovic strike at the Karadjordje stadium.
But they hit back with two opportunist efforts by attacking midfielder Miroslav Stevanovic, a promising 20-year old Bosnian prospect who made the most of a rare start after he replaced the suspended Nikola Lazetic.
