Juventus star Arturo Vidal and Napoli's Eduardo Vargas struck in the second half to give the Chileans a winning start in Group A as they chase a first Copa America crown in 99 years of trying.
Vidal bounced back from the disappointment of last week's Champions League final defeat to Barcelona to bury a 67th-minute penalty before Vargas sealed victory six minutes from time.
Roared on by a passionate home crowd in Santiago, Chile began at a furious pace, twice threatening in the opening minutes after slicing Ecuador open.
Dominguez was pressed into action by Sanchez again moments later, but the tall goalkeeper judged the striker's attempted lob and gathered with ease.
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After surviving the early onslaught, Ecuador gave Chile a scare at the other end on 18 minutes when Fidel Martinez pounced on slack defending to draw a fine save from Barcelona goalkeeper Claudio Bravo.
Ecuador continued to frustrate the home side but Chile always looked the likeliest to score, Sanchez again going close with a shot that rolled just wide on 39 minutes.
Yet Chile stepped up the pace, threatening through Vidal and Vargas before the game's turning point when Vidal burst into the box and was tugged down by Miller Bolanos.
Argentine referee Nestor Pitana pointed to the spot immediately and Vidal stepped up to blast the spot kick high and wide past Dominguez.
Valencia almost grabbed an equaliser shortly afterwards when his looping header crashed off the crossbar but moments later Chile made the game safe when Sanchez released to Vargas who slid his shot beneath Dominguez for 2-0.