It also means France are not yet confirmed qualifiers for the knockout stages despite their two comfortable victories so far.
Both sides missed chances to take an early lead before Valencia could only fire wide once he had been freed with a long ball forward.
It was another lump forward that undid Ecuador as they failed to deal with a long kick from Alexander Dominguez with Costly collecting the loose ball and firing home to open the scoring between the two group outsiders.
It was Honduras' first World Cup goal in 32 years but their joy at leading the game was short-lived as the in-form Valencia reacted quicker than any of the Honduras backline to convert Juan Paredes' deflected shot just three minutes after Ecuador had fallen behind.
Honduras came close to re-establishing their lead before the interval as Victor Bernardez saw a free-kick well saved by Dominguez before Costly hit the bar with a close-range header in first-half stoppage time.
Jerry Bengston bundled home the rebound but saw the goal rightly chalked off for handball, with the New England Revolution striker booked as a result.