Internacional blitzed Tigres UANL early in its Copa Libertadores semi-final first leg, and then held on for a 2-1 win.
Andres D'Alessandro and Valdivia's goals inside the first 10 minutes set the match up for the host in Porto Alegre, but Tigres fought back to only trail by one goal heading to the second leg in Mexico.
Hugo Ayala pulled a goal back in the 23rd minute, but Internacional held on to take the lead back to the Estadio Universitario de Nuevo Leon next week.
D'Alessandro broke the deadlock in the fifth minute, getting on the end of a Nilmar pass and finishing with power from outside the area past Tigres goalkeeper Nahuel Guzman.
Valdivia then produced a sterling effort - also from outside the area - as he lifted an effort over Guzman, who was off his line.
Ayala got the men in yellow back in the game, his header from Rafael Sobis's cross beating Alisson in Internacional's goal.
However, the centre-back turned villain when he received a second yellow card in the 58th minute, making Tigres's challenge all the tougher - and ruling Ayala out of the return leg.