De Nigris scored from a header in the 42nd minute and had the final say with another goal in the 89th minute. Wales manager Chris Coleman remained without a victory since taking over the national side following the death of former Wales manager Gary Speed last November.
Liverpool's 32-year-old forward Craig Bellamy played the full match for Wales. Wales will host Bosnia-Herzegovina in August before beginning their FIFA World Cup qualifying campaign against Belgium in September.
The Mexicans will face Bosnia-Herzegovina in Chicago on Thursday and Brazil next Sunday in Arlington, Texas, before starting FIFA World Cup qualifying at Mexico City against Guyana on 8 June.