Veteran forward Clint Dempsey (22nd minute) and Gyasi Zardes (65th) scored on either side of the break to ensure that the hosts earned their first berth in the Copa America semi-finals since 1995.
Antonio Mina (74th) reduced the deficit for Ecuador late in the second half to give the South Americans a glimmer of hope.
US will face either Argentina or Venezuela in the last four stage next week.
Argentina and Venezuela will play their semi-final on Saturday.
This was the second appearance in the Copa America quarter-finals for the US. They beat Mexico in their first appearance in the knockout stage during the 1995 edition.