Chile took the lead in the eighth minute when Jose Fuenzalida volleyed into the net but Ecuador were awarded a penalty when goalkeeper Gabriel Arias clattered Jhegson Mendez, allowing Enner Valencia to level from the spot in the 26th.
Sanchez, who had ended a barren five-month spell by scoring in Monday's 4-0 win against Japan, put Chile ahead early in the second half, expertly guiding a bouncing cross into the net with one touch.
Ecuador, who were hammered 4-0 by Uruguay in their opening game, rarely threatened again and saw defender Gabriel Achilier receive a straight red card in stoppage time for a rash tackle on Arturo Vidal, who had to be taken off.
Sanchez later revealed he had been playing with an ankle injury sustained in the first half.
"After a cross I rolled my ankle but I put a bandage on it, I took a pill for the pain and I came out again," he told reporters.
"I think I have a sprain, I was playing with pain but I hope it's not too serious."
Chile coach Reinaldo Rueda praised Sanchez for playing on, adding that the ankle was not the same one he injured in May.
"He was evaluated by the doctors at halftime who said he could continue, although he put lots of ice on it at halftime. He made a huge effort in the second half," he said.
"We'll evaluate it again but we hope it isn't serious."
Chile, Copa champions in 2015 and 2016, lead Group C on six points. Uruguay are second on four with Japan third on one and Ecuador bottom with no points.
Ecuador still have an outside chance of sneaking into the quarter-finals as one of the two best ranked third-place finishers but they must win their game against Japan on Monday and hope other results go their way.
Their coach, Hernan Dario Gomez, gave the briefest of post-match news conferences, saying he was not in the mood to take questions and gave a short assessment of the game before leaving.
(Editing by Peter Rutherford)
