Spain coach Vicente del Bosque had left a number of regulars at home and used the game to give squad players a run-out with three under-21 internationals making their senior debuts.
Barcelona winger Cristian Tello, who set up Cazorla's goal, Real Sociedad defender Inigo Martinez and Atletico Madrid midfielder Koke all featured in a game dominated by the visitors.
"It was a tough game. They were very physical but we developed our play and were able to achieve the win," Tello, who played the full 90 minutes, told Spanish broadcaster Telecinco.
"To play with the senior team is a dream come true and I hope I will be able to play many more times with them."
Spain, playing their first game since losing the Confederations Cup final 3-0 to Brazil in June, took control of the match while the hosts looked for chances on the break or from set pieces.
The game was halted briefly in the 11th minute as fans at the Monumental stadium rose to pay tribute to Ecuador forward Christian Benitez who died last month of a heart failure aged 27.
Benitez, who wore the number 11, had scored four goals in their World Cup qualifiers, making him Ecuador's second top scorer in the campaign.
Spain's David Silva and Andres Iniesta struck the post early on but it was Cazorla who made the opening for the first goal when his long-range shot was only parried.
The Arsenal midfielder picked up the rebound and squared for Negredo to score his seventh goal in 15 appearances with the coolest of touches.
Spain keeper Iker Casillas turned a fierce drive from Segundo Castillo round the post just before the break and Enner Valencia headed against the Spanish woodwork in the second period, as the game was disrupted with substitutions.
Tello's neat backheel set Cazorla free into the area to score the second, crowning an impressive performance from the diminutive playmaker.
Spain and Ecuador are both on course to qualify for next year's World Cup finals in Brazil.
Spain top European Group I with 11 points from five games, a point ahead of France, and they play third-placed Finland in Helsinki next month.
Ecuador are third in the South American qualifying group behind Argentina and Colombia.
(Writing by Mark Elkington in Madrid, editing by Ken Ferris)
