The match was the 134th and final international for Sneijder, the 34-year-old former Real Madrid, Inter Milan and Ajax star. It was also an important warmup for the Netherlands' first UEFA Nations League match - on Sunday against World Cup champion France at Saint-Denis.
The Dutch were sloppy in the first half and Pedro Aquino outjumped Daley Blind for a corner to give Peru a 1-0 lead in the 13th minute.
Depay equalized on the hour after Frenkie de Jong, making his international debut as a second-half substitute, won the ball and drilled a quick pass to the Olympique Lyon striker.
Sneijder was substituted immediately after the goal, hugging all his teammates as he left the pitch to cheers of "Wesley thanks!" from the crowd at the Johan Cruyff Arena.
"It's over, it's done. My last match ... in the orange shirt," Sneijder said. "Everything comes to an end."
Depay then ensured Sneijder's finale would be a win by volleying home Quincy Promes' blocked shot in the 83rd minute.
At a ceremony after the match, fans slapped their heads, mimicking Sneijder's celebration when he scored a header winner against Brazil in the World Cup quarterfinal in South Africa.