The striker finished with aplomb in the 58th minute, after controlling a long ball forward from Thiago Silva.
The Selecao was struggling to break down its European opponents when, in the 58th minute, the forward expertly controlled a long ball forward from Thiago Silva before prodding home.
Brazil had chances to add to its tally but was ultimately forced to settle for a narrow win.
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Having not been tested by Panama in midweek, the World Cup host was at full strength for the clash against Ljubinko Drulovic's side.
It was restrained for large spells, however, and coach Luiz Felipe Scolari will be aware improvement is required despite Fred's well-taken winner.
Brazil's victory may do little to fill an expectant nation with great confidence. However, with Neymar getting almost 80 minutes of action on his road to full fitness and Fred scoring his first in Brazil colors since the Confederations Cup, there are reasons for the hosts to be optimistic.
After a lively opening from both sides, Aleksandar Kolarov threatened first when he struck an effort wide of Julio Cesar's left-hand post after nine minutes.
Neymar then almost benefited from a block that fortuitously landed in his path - only for Ivanovic to produce a well-timed last-ditch tackle.
A combination of tenacious and robust defending helped keep Brazil's forwards well shackled, although Fred was next to threaten - his dipping strike veering off target 24 minutes in.
David Luiz was forced into a hurried clearance following Kolarov's fierce delivery before Aleksandar Mitrovic wasted the best chance of the half, heading wide with the goal at his mercy.
Luiz and Thiago Silva, who will team up at Paris Saint-Germain from next season, then got mixed up close to halftime, but an offside flag rescued Brazil as Lazar Markovic converted.
Scolari swapped Oscar for Willian at the break, presumably in an effort to shake things up, but Brazil still looked somewhat out of sorts.
Indeed, Dusan Tadic perhaps could have opened the scoring for Serbia had he gambled on reaching a cross lofted into the hosts' box.
Fred subsequently ensured first blood went to Brazil, the striker cleverly chesting Thiago Silva's delivery to take Branislav Ivanovic out of the game and then prodding the ball past Vladimir Stojkovic - despite having stumbled before doing so.
Neymar, lively but far from his dangerous best, then flashed an effort over the crossbar as his side sought to make the scoreline more emphatic.
There were to be no more goals, although Serbia's Milos Jojic and Brazil forward Jo hit the woodwork in the closing stages.
Brazil open its World Cup campaign against Croatia on June 12 and will be hopeful of a more fluent display.