Colombian Osorio, who took Mexico to the round of 16 at the World Cup in Russia this year before losing to Brazil, had looked set to make a winning start in his new job.
But Belgium-based Tau, who is fast developing into the star of the South African team, ran on to a Thulani Serero pass and dinked the ball over goalkeeper Antony Silva to equalise in the final moments.
Paraguay should have been more than one goal ahead at half-time at Moses Mabhida Stadium in the Indian Ocean port city as they were denied twice by the woodwork.
The South Americans went ahead on 32 minutes when Federico Santander from Serie A outfit Bologna tapped the ball into the net after Darren Keet parried a Cecilio Dominguez cross.
"Wasting scoring chances cost us victory," Osorio said after a match staged in honour of former South African president Nelson Mandela, who died in 2013 aged 95.
"South Africa were a strong physical team who posed problems for us and I learnt a great deal from my first match in charge of Paraguay."
Bafana-Bafana coach Stuart Baxter said his South African side faced aggressive, well-prepared opponents on a badly cut-up surface.
"It must have felt like going to school for many of my players, they are not used to facing the challenges created by a South American side.
"What pleased me was we never gave up as the clock increasingly became our enemy, and might have scored before Percy equalised."
In the Tunis suburb of Rades, Morocco edged Tunisia 1-0 through a Youssef en-Nesyri goal to complete contrasting international windows for the north African teams.
Last Friday, Morocco won 2-0 at home to Cameroon and Tunisia lost 3-2 away to Egypt in 2019 Africa Cup of Nations qualifiers.
Tunisia dominated possession against Morocco only to be undone by the opportunism of Leganes forward En-Nesyri four minutes before half-time when he netted off a rebound.
Nigeria were held 0-0 by Uganda before a capacity 22,000 crowd at a stadium in southern city Asaba named after Nigerian football legend Stephen Keshi, who died two years ago aged 54.
A lively match produced plenty of goalmouth action with Ugandan Omar Magoola, who plays for leading Sudanese club Al Merrikh, the much busier goalkeeper.