North End started the brighter of the two sides and led as early as the 11th minute at Deepdale.
After goalkeeper Wes Foderingham, so impressive in Swindon's midweek cup defeat to Chelsea, could only tip Kevin Davies' fierce effort into the air, Hume was on hand to nod in from close range and give the home side the lead.
Preston started the second half just as positively as they did the first and once more they got their reward for their dominance, although this time in bizarre circumstances.
With the ball bouncing harmlessly across goal, McEveley's attempt to pass the ball back to Foderingham saw him somehow chip the ball over the stranded stopper and put North End two-nil to the good.
Swindon rallied in a bid to fight their way back into the game and Dany N'Guessan's curling effort from the edge of the area gave them hope late on but Preston hung on for another victory.