Valencia scored an early penalty and added a well-taken 31st-minute header to give the South Americans a commanding first-half lead as the Qataris looked overcome by the significance of the occasion.
"Obviously this was not what we were hoping for," Qatar coach Felix Sanchez said.
"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."
It could have been even worse for the hosts in front of a 67,372-fan crowd at the Al Bayt Stadium had Valencia, 33, not had a third-minute header disallowed for a marginal offside after goalkeeper Saad al-Sheeb had flapped at the ball.
It was al-Sheeb who later tripped Valencia when he was through on goal and then dived the wrong way as the Ecuadorian calmly 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 al-Sheeb 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."
That goal killed the game as a contest, and the second half was played at a slow pace, with many Qatar fans leaving before the end as Ecuador's fans chanted "Olé!"
Despite an enviously long time to bond and train together, including summer camps in Europe, Qatar looked largely toothless. 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.
Ecuador are dreaming of surpassing their best previous World Cup showing, when they reached the last 16 in 2006.