A Selecao went ahead in the first half through Jadson, but goals from Roque Santa Cruz and substitute Nelson Haedo Valdez looked set to claim a shock win for Paraguay until Fred's late effort.
Paraguay had the better of the opening exchanges, with Blackburn Rovers striker Santa Cruz having the first chance in the second minute from Lucas Barrios' assist, although the shot went over the crossbar. But it was Brazil who went ahead six minutes before the interval when Jadson's strike from distance beat Paraguay goalkeeper Justo Villar.
Santa Cruz, Valdez strike
Brazil coach Mano Menezes then replaced Jadson with Elano at the start of the second half as they looked to ramp up the pressure on their opponents. Instead, Paraguay equalised in the 54th minute after a great run by Marcelo Estigarribia was finished by Santa Cruz.
Fans hoping to see Valdez introduced to the action had their wish soon after when the Hercules forward came on in place of Barrios. And he made his mark after 65 minutes to fire Paraguay in front.
An error by Brazil right-back Dani Alves allowed Cristian Riveros to pick up the ball and supply a pass to Valdez, who let fly with a shot. Defender Lucio tried to clear, but could only hit Valdez in the chest before the ball rebounded into the back of the net.
With nine minutes remaining, Menezes decided to replace youngster Neymar with Fluminense striker Fred in a bid to get something from the game. And the former Lyon player repaid the faith with an equaliser a minute before time, turning in a neat flick from Paulo-Henrique Ganso.
Fred aiming for more
Brazil, winners of the Copa America in 2004 and 2007, still have work to do to reach the quarter-finals and Fred admits not everything has gone to plan. "We should think as a group," he said. "We are having some difficulties in our games. I will keep trying to score goals, important goals, for Brazil."
Paraguay coach Gerardo Martino, meanwhile, believes his team have shown themselves to be worthy opponents. "We have proved our temperament," he said. "We should have won the two games we played. I always think we should improve our ball control. We have to encourage ourselves to attack more when we play big teams."