The visitors were the better side after the break and after Kohr had a goal chalked off for offside, Silva gave them a deserved lead in the 61st minute with a thumping back-post header from Filip Kostic's pinpoint cross.
Real Valladolid had better attacking plays; however, it could not reach keeper Tomas Vaclik's net too many times.
The Portuguese went into defending mode for the final 15 minutes as Italy's Simone Zaza sought desperately for the equaliser.
Germany crashed out of the World Cup following their 0-2 defeat against South Korea.
The defending European champions, who face Spain, Morocco and Iran in Group B, largely flattered to deceive.
"When you score four goals away from home, you're always likely to win," Theo Walcott said.
