De Canio took over at Loftus Road this week and saw plenty to encourage him as the R's extended their unbeaten run to five matches.
Rangers gave a debut to playmaker Akos Buzsaky, who was signed from Plymouth just before De Canio's appointment as first-team coach.
Buzsaky, wearing QPR's coveted number 10 shirt - previously worn by legends Rodney Marsh and Stan Bowles - showed some nice touches and had an early long-range shot pushed away by goalkeeper Boaz Myhill.
But it was on-loan West Ham winger Ephraim who gave Rangers the crucial breakthrough on 26 minutes.
He collected Martin Rowlands' pass and drilled the ball into the bottom corner from the just outside the box.
Hull's Dean Windass fired just wide before the break, but Rangers were rarely troubled by the Tigers and went further ahead 11 minutes into the second period.
And their second goal was just as spectacular as the first.
Leigertwood, who produced a fine display in midfield, gathered the ball just inside the Hull half and stormed towards the edge of the penalty area before curling an unstoppable curling shot beyond Myhill.
Nigerian star Jay-Jay Okocha, back in the Hull side after injury, made virtually no impact and was substituted with 18 minutes remaining.
Rangers keeper Lee Camp did have to make one important late save, when he dived to his left to tip Dean Marney's shot to safety.