Kandol's treble came in the space of little more than 10 minutes and both he and Showunmi - the goalscorers who secured last week's second-string win at Middlesbrough - again staked their claim for greater involvement with United's first XI.
Showunmi scored twice in the first half, his second goal coming through a powerful header from Andy Robinson's corner, but a foul by Robinson inside United's area saw Ian Morris pull a goal back from the penalty spot before half-time.
Scunthorpe's reply appeared to set the stage for a competitive second 45 minutes, but Showunmi added his third goal soon after the restart.
Kandol then got in on the act, scoring for the first time in the 71st minute, and the Congolese international turned home a clever pass from Showunmi before driving home a late penalty to seal a rampant win.
Leeds' captain Richard Naylor made his first 90-minute outing of the season, but left-back Ben Parker - out since the first weekend of the term with a hamstring strain - was not involved.
Leeds Reserves: Ankergren, Darville, Milne, Naylor, L Turner, Falkingham, Prutton (Hatfield 67), Kilkenny, Robinson, Showunmi, Kandol.
Unused Subs: R Jones, Whitwell, Watson, Booker.