The England striker's halftime introduction energized United and he pounced when a clearance from Ryan Bennett deflected into his path, rounding goalkeeper John Ruddy to slot home.
"He changed the game when he came on," Moyes said. "He is doing very well, and we need everybody to chip in with goals when Wayne Rooney and Robin van Persie are out."
United is provisionally sixth in the standings, two points off the top four.
Hull's thrashing of sorry Fulham was notable for the eye-catching celebration by Tom Huddlestone, who marked his first goal since 2011 by letting club physio Rob Price cut off a piece of his hair on the sideline. The midfielder had pledged not to cut his hair until he scored again.
Fulham has looked an improved side under new manager Rene Meulensteen but this defeat -- its worst in the Premier League era -- was a major setback against a team which has often struggled for goals this season.
"I'm shocked," Meulensteen said. "I don't know if there was something in the tea. I did not see that coming and the players did not see that coming."
All of Hull's goals came in the second half, with captain Robert Koren scoring twice and Ahmed El Mohamady, George Boyd and Matt Fryatt also netting.
West Ham was denied victory by Saido Berahino's 69th-minute goal at Upton Park.
Former France striker Nicolas Anelka scored twice for West Brom and appeared to celebrate his first by performing an anti-Semitic salute used by French comedian Dieudonne M'bala M'bala. Jewish groups in France have linked the "la quenelle" gesture -- which they claim is a Nazi salute in reverse -- to anti-Semitic incidents in the country.
"It is dedicated to a French comedian he knows very, very well," West Bromwich Albion coach Keith Downing said of Anelka's celebration. "He uses it in his act and I think speculation (that it is anti-Semitic) can be stopped now, it is absolute rubbish really."
