Didier Drogba gave the Elephants the lead early in the second half and former England coach Eriksson, taking charge for the first time less than two weeks before the start of the World Cup, looked set to celebrate a win when substitute Souleymane Bamba made it 2-0.
Argentine-born Lucas Barrios pulled one back with his second goal in as many appearances for the South Americans, who began with a second string line-up, and Aureliano Torres snatched a last-gasp equaliser with a deflected free kick
The substitutes' benches were too small for the delegations and the Paraguayan reserves watched the match among the crowd in the only stand, with a superb view over Lake Geneva.
"I think we did well it the first half and the beginning of second half, probably we should have scored more goals," said Eriksson.
"We created a lot of chances, in the last 30 minutes we lost organisation in our team, we didn't keep possession as well.
"We have to play better, we will play better, we have worked one week with all the players. It's about organisation, defending well together, attacking well together, we're working every day on that."
Aruna Dindane shot wide after bursting through the Paraguay defence but the best first-half chance fell to Drogba, who dived in to meet Chiek Ismael Tiote's cross but directed his header just wide of the goal.
Drogba's persistence paid off when he scored with a free kick in the 54th minute, a deflection wrong-footing Villar.
