Fenerbahce attacker Enner Valencia netted an early one for Ecuador in the 3rd minute before it was disallowed by the video assistant referee (VAR) at Al Bayt Stadium.
Valencia again put the ball into Qatar's net, with a penalty kick, in the 16th minute, and then in the 31st, he scored again with an accurate header.
Valencia walked off from a light injury in the 43rd minute, and the first half ended 2-0, despite Qatar's better display after the second goal and Almoez Ali missing a critical shot in the final seconds.
Pedro of Qatar wasted another important goal chance in the 61st minute.
Enner Valencia substituted in the 77th minute, coming off the bench with applause.
After a long shot by Qatar's Muntari missed the Ecuador goal by inches in the 85th minute, the game ended 2-0 for Ecuador.
Wtih this result, Qatar became the first hosts in the history of the World Cup to lose the opening match.
Ecuador now leads Group A of World Cup with 3 points while Qatar placed fourth with zero.
Senegal will take on the Netherlands in the next Group A match on Monday.