Paraguay could only cheer after losing to Colombia in Group B on Sunday, but it got the result it needed to advance as one of the top two third-place finishers.
Uruguay won Group C after beating second-place Chile 1-0 in Rio de Janeiro on Monday. It ended with seven points, one more than two-time defending champion Chile. Guest Japan finished with two points and Ecuador with one.
The top two nations in each of the three groups advanced, along with the two best third-place finishers.
The quarterfinals will feature Brazil-Paraguay, Venezuela-Argentina, Colombia-Chile and Uruguay-Peru.
It was an open match at the Mineirao Stadium as only the victory would suffice for Japan and Ecuador.
Japan opened the scoring in the 15th minute with a goal initially disallowed for offside but later confirmed by video review. Ecuador goalkeeper Alexander Dominguez couldn't fully clear a deep pass into the area and Shoya Nakajima picked up the loose ball and lobbed a shot into the open net.
The goal had been called off because Shinji Okazaki appeared to be offside when he made a run into the area.
Ecuador equalized in the 35th with a close-range shot by Angel Mena. Japan goalkeeper Eiji Kawashima made a great one-handed save after a shot by Robert Arboleda, but Mena picked up the rebound and easily found the net.
Japan forward Daizen Maeda had a great chance to break the deadlock near the end of the match, but his shot from inside the area was stopped Dominguez's boot.
In stoppage time, Ayrton Preciado narrowly missed for Ecuador, and Japanese teenager Takefusa Kubo had a goal disallowed for offside just before the final whistle.
Kubo, an 18-year-old forward signed by Real Madrid for its "B'' team, was one of the many youngsters Japan brought to Brazil to prepare for the Olympic tournament at home next year.
Japan last played in the Copa America as a guest in 1999, when it also was eliminated in the group stage.
Ecuador has won only two of its 18 matches in the Copa America since 2004. It lost to Uruguay and Chile in its other matches this year. Japan's youngsters lost to Chile and drew with Uruguay.