Saturday's result left 1991 European Cup winners Red Star three points adrift of bitter city foes Partizan with three matches remaining and an uphill task of retaining the title.
"The club's emergency board convened and decided to name Gjurosvki as the head coach until the end of the season," Red Star said on their official website (www.crvenazvezdafk.com) several hours after Bozovic stepped down.
It will be a second stint for 55-year old Macedonian Gjurovski at Red Star's helm, having guided them to the 2007 domestic double after winning four Yugoslav league titles with them as a player in the 1980s.
He also coached the Macedonian national team from 2013 to 2015 before a short stint at Japanese side Nagoya Grampus Eight last year.
Bozovic came under pressure after Red Star were beaten at home by Partizan 3-1 on April 18, having looked certain to win their 28th league title midway through the season before throwing away a substantial lead in the standings.
Should Partizan win the title, they would equal Red Star's tally of 27 in the perennial battle of Serbia's big two for local supremacy.
"I hope my resignation will shake up the team and although I doubt they can now overhaul Partizan in the league run-in, they can still win the Serbian Cup," Bozovic told a news conference.
Red Star hold a 4-1 first leg advantage over Cukaricki in the Cup semi-finals and could meet Partizan in the final as the holders are at home to Vojvodina Novi Sad after a 0-0 draw in the opening leg of their tie.
(Writing by Zoran Milosavljevic; Editing by Toby Davis and Pritha Sarkar)
