Sanchez tapped in an 85th-minute winner to lift Juan Antonio Pizzi's men to a much-needed victory at the Estadio Monumental David Arellano.
Eduardo Vargas's opener appeared to be sending the host to a win before debutant Romario Ibarra's equaliser silenced the home crowd with six minutes remaining.
However, Chile responded immediately as Sanchez struck to give his side a deserved win.
Chile's win, combined with other results on matchday 17, saw Pizzi's side move into third in the standings with one game remaining.
However, Chile's final outing is a trip to Brazil on Wednesday (AEST) and it will be without Arturo Vidal after the midfielder picked up a yellow card.
Sanchez, Vidal, Vargas and Gary Medel all started for Chile, who entered the clash on a three-match losing run.
In his first match in charge, Jorge Celico made huge changes at Ecuador, which sacked Gustavo Quinteros after back-to-back losses last month.
Celico made six changes to the starting XI that lost at home to Peru, with Dario Aimar, Michael Arroyo, Renato Ibarra, Ayrton Preciado, Jefferson Intriago and Roberto Ordonez starting in place of Gabriel Achilier, Pedro Velasco, Christian Noboa, Juan Cazares, Felipe Caicedo and Enner Valencia.
In front of an energetic home crowd, Chile made a good start, with Sanchez heavily involved in the opening stages.
But the host struggled to get in behind, although Vidal threatened as his strike from just inside the area was blocked in the 13th minute.
Just nine minutes later, Chile deservedly went ahead.
Sanchez won possession in attack and Valdivia capitalised, the attacker cutting back a pass to Vargas, who took a touch before firing into the roof of the net from near the penalty spot.
Chile continued to dominate proceedings and almost doubled its lead four minutes before half-time after a wonderful team move.
Sanchez was at the centre of it, the Arsenal star completing his run with a pass to Valdivia, who found Eugenio Mena – but he fired just wide from the left side of the area.
The hosts should have gone 2-0 up in the 49th minute, but Valdivia headed a pinpoint Vidal cross over the bar from six yards.
Vidal was booked just before the hour-mark in a blow to Chile, who conceded an equaliser in the 84th minute.
Ibarra timed his run into the area to perfection to side-foot in a stunning equaliser.
However, Chile quickly restored their lead with what proved to be the match-winner.
Vidal dispossessed an Ecuador defender and teed up substitute Felipe Gutierrez, whose shot was saved by Maximo Banguera and into the path of Sanchez to tap in.