A draw would have done against Senegal, but Ecuador paid for two lapses in concentration.
Ecuador need to win or draw to progress but will remain in contention if they lose and Qatar upset the Dutch, who were leading 1-0 at halftime.
The result means hosts Qatar have been knocked out from the tournament.
One of the pandas sniffed at the two flags and then placed its paw on the Ecuador flag, thus predicting that the winner could be Ecuador.
The striker nicknamed 'Superman' scored a brace to help his side to 2-0 win over Qatar.
Captain Enner Valencia scored both goals in the first half.
Two rival fans shared a beautiful moment at full-time at Al Bayt Stadium on Sunday.
Valencia drew first blood from the penatly spot in the 16th minute. He doubled the lead with a fine header in the 31st.
The opening ceremony will be held at the 60,000-capacity Al Bayt Stadium located 40km north of Doha.
The more daunting prospects of African champions Senegal and perennial powerhouse the Netherlands await them next.