Ecuador lost 2-1 to Peru when the two teams met in Madrid on Sunday and they were second best for long periods in the rematch.
But they took the lead with practically their first clear chance of the game five minutes from time when Benitez took advantage of some slack marking from the Peru defence to crack home after a corner.
Further sloppy defending allowed De la Cruz to add a second deep into injury time, the Reading defender racing clear from 40 metres out and then drilling an angled shot below keeper George Forsyth.
The Copa America kicks off on June 26. Peru have been drawn in Group A with hosts Venezuela, Bolivia and Uruguay, while Ecuador are in Group B with Brazil, Mexico and Chile.