It could have been even worse for the hosts in front of a 67,372 crowd at the tent-shaped Al Bayt stadium had Valencia, 33, not had a third minute header disallowed for a marginal offside after goalkeeper Saad Alsheeb had flapped at the ball.
It was Alsheeb who later tripped Valencia when he was through on goal and then dived the wrong way as the Ecuadorean coolly dispatched the resulting penalty in the 16th minute.
For his second, Valencia was unmarked but still showed great technique to stoop and take Angelo Preciado’s cross almost from behind him to head past Alsheeb again.
“I dreamt so many times about winning this opening match. This was a dream that I managed to score and help my team get the three points,” Valencia said.
“We managed to score a couple of quick goals which helped us to get control of the game and win the three points ... We think we can go very far and perform well.”
The 33-year-old scored all of Ecuador’s three goals at their last World Cup appearance in 2014 and Sunday’s double cemented his status as national hero.
His second goal killed the Group A game as a contest and the second half was played at a slow pace, with many Qataris leaving before the end as Ecuador’s fans chanted “Ole!”
Qatar looked largely toothlessdespite an enviously long time to bond and train together, including summer camps in Europe. Almoez Ali had their best chance at the end of the first half, heading wide but then judged offside.
Mohammed Muntari also fired over in the dying minutes.
Qatar coach Felix Sanchez looked increasingly disconsolate watching his nervous-looking players misplace passes and allow Ecuador to outmuscle them easily from front to back.
Both sides now have to play Senegal and the Netherlands in the group stage, with Qatar’s chances of picking up points or qualifying looking slim on this performance.
“Obviously this was not what we were hoping for,” Spaniard Sanchez said of Sunday’s curtain raiser for the tournament.
“There is no excuse, I want to congratulate our opponents Ecuador. There is a lot of room for improvement.
“We did not play at our best level. Maybe the responsibility and the nerves got the better of us. We just have to let go and forget about it and be more competitive. We can do it.”
At their fourth World Cup, Ecuador are dreaming of surpassing their best ever previous showing at the finals when they reached the last 16 in 2006.
Coach Gustavo Alfaro will be happy that his players put aside the furore over defender Byron Castillo, who was left at home to avoid further controversy after they faced possible expulsion in a complaint by Chile over his nationality status.