Tevez and his beaten team-mates could miss out on South Africa, with Argentina now facing huge pressure from Colombia and Ecuador for the fourth qualifying berth in South America.
Robi had one of his quieter games for Brazil but Dunga's group leaders still clinched their ticket with goals from Luisao and a double from striker Luis Fabiano against their old rivals.
Tevez was lively but came in for some harsh treatment - including a clattering from Elano - and was replaced before the end with a pivotal game at Paraguay to come on Wednesday night.
He will not want to be part of an Argentina side that misses out on the finals for the first time since 1970, while mentor Diego Maradona's reign as coach is now under real threat.
City team-mates Gareth Barry, Shaun Wright-Phillips and Joleon Lescott helped England warm up with a 2-1 victory over Slovenia at Wembley before Wednesday's clash with Croatia.
SWP and his right-side rival Aaron Lennon played a half each, Lescott replaced Matthew Upson for the last 25 minutes, and Barry was widely praised for his midfield endeavours.
Shay Given's Republic of Ireland won 2-1 in Cyprus to keep alive their hopes of qualification.
Elsewhere, Vladi Weiss played 73 minutes of Slovakia's 2-2 draw with Czech Republic and Martin Petrov helped Bulgaria to a much-needed 4-1 win over Macedonia in Ireland's group.
Kolo Toure stayed solid in the Ivory Coast's 5-0 win over Burkina Faso. Nigel de Jong had a hand in Robin van Persie's opening goal of Holland's 3-0 friendly win over Japan.