Valencia, after previously seeing an early header ruled out through VAR, gave Ecuador a deserved lead from the penalty spot after 16 minutes, before following his effort from 12 yards with a brilliant header shortly after the half-hour mark.
Qatar, who were playing a World Cup fixture for the first time, had fleeting moments going forward, but the Asian nation were thoroughly outclassed for large periods of the Group A fixture in Al Khor and become the first World Cup hosts to lose their opening match.
The build-up to the tournament in Qatar has been plagued by controversy and talking points, and it took just minutes for that to transfer itself onto the pitch.
Enner Valencia had appeared to give Ecuador a third-minute lead with a close-range header, only for VAR to rule that there had been an offside in the build-up, leaving supporters and viewers perplexed.
Fifa revealed 10 minutes later that the shin of Michael Estrada had been offside before the ball had been scissor-kicked into Valencia's path, but Ecuador were still able to get their noses in front by the 16th minute.
The decision-making of Qatar goalkeeper Saad Al Sheeb had led to the chain of events which accompanied the disallowed goal, and another rash call led to him hauling down Valencia as he attempted to take the ball past him.
After Al Sheeb was booked for his troubles, Valencia got to his feet to dispatch the penalty with unwavering confidence, passing the ball into the bottom corner as Al Sheeb dived the other way.
Despite a lively opening half-hour which included three yellow cards, Ecuador were dominating, and it was not long before Valencia doubled his team's advantage.
A magnificent cross from the right from Angelo Preciado found the Fenerbahce man, who directed a pin-point header into the bottom corner of Al Sheeb's net from 12 yards.
In the final seconds of five minutes of added-on time, Qatar could have halved the deficit only for Almoez Ali to send a free header wide of the post.
After that opportunity had gone begging for Qatar, Ecuador were able to remain in control after the restart without looking particularly threatening in search of a third goal.
Romario Ibarra saw a curling effort palmed away by Al Sheeb, while Qatar's second chance of the game arrived in the 63rd minute as Ro-Ro powered a header wide of the post after meeting a diagonal ball.
With 15 minutes remaining, Ecuador were dealt a blow when Valencia was forced to hobble off, the double-goalscorer having sustained what appeared to be a knee problem during the first half.
To Qatar's credit, they performed much better than in the opening period, and Mohammed Muntari sent a shot over Hernan Galindez's crossbar after latching onto a ball over the top.
Nevertheless, it was a rare moment of encouragement for one of the minnows of the competition, who are already facing an uphill battle to avoid being eliminated ahead of the knockout rounds.
The other opening fixture in Group A takes place on Monday as Africa Cup of Nations champions Senegal take on three-time World Cup runners-up Netherlands.