Coach Radomir Antic rested defensive stalwart Nemanja Vidic and the back four looked all at sea in the opening 30 minutes, only two superb saves by reserve goalkeeper Bojan Isailovic keeping Serbia on level terms.
Goals from Enrique Vera and Lucas Barrios gave Paraguay a 2-0 win over Greece in a warm-up match between the two World Cup-bound sides.
With the deadline for naming 23-man squads for the finals now passed, Italy coach Marcello Lippi was mulling over taking midfielder Andrea Cossu as a 24th man if Mauro Camoranesi's knee injury does not improve.
Camoranesi was included in the world champions' 23-man squad but can be replaced before the first match.
European champions Spain, fancied by many to win a first World Cup, plan to give midfielder Cesc Fabregas a run-out in a warm-up against South Korea on Thursday.
The midfielder has been recovering from a cracked bone in his right leg and has not played for two months. Striker Fernando Torres is close to a return from a knee injury but must wait a little longer for playing time, coach Vicente del Bosque said.
Brazil’s flair to the fore
Brazil gave a glimpse of the Latin American flair they will bring to the World Cup in South Africa with a 3-0 warm-up win over Zimbabwe on Wednesday, a victory tempered by an injury to goalkeeper Julio Cesar.
While Brazil enjoyed a rapturous reception at the 60,000 capacity national stadium in Zimbabwe's capital Harare, FIFA president Sepp Blatter was attending the official handing-over of the showpiece Soccer City stadium near Soweto, venue for the World Cup's opening match on June 11 and final on July 11.
The Swiss head of soccer's governing body described the 90,000-capacity stadium as a magnificent flagship for Africa.
Former South African president Nelson Mandela, 91, is expected to be among the VIPs at the opening match between South Africa and Mexico although ill-health could prevent him from attending.
"The right legacy for this event will be 'let's celebrate Africa's humanity'," Blatter said.
"Let's celebrate the most charismatic humanist alive -- Nelson Mandela. We do hope Nelson Mandela will be here at the beginning of the World Cup in this stadium. This will be the highlight."
Brazil, who will attempt to win the World Cup for the sixth time, were given a decent workout by Zimbabwe, ranked a lowly 110th in the world.
"In friendlies, the result is the least important," midfielder Elano told reporters. "The important thing today was that we played well and I think the fans were satisfied with the spectacle."
Michel Bastos, Robinho and Elano scored for Dunga's side, although the coach would have been concerned by the sight of ’keeper Julio Cesar being substituted in the 26th minute.
Brazil doctor Jose Luis Runco said the Inter Milan ’keeper had been taken off as a precaution after hurting his back.