Leading at half-time through a header from skipper Rob Jones, doubles from Abdessalam Benjelloun and Steven Fletcher emphasised Hibs' supremacy.
Both teams had to cope with a blizzard which swirled around Hampden for the first half-hour.
Kilmarnock had the first chance when Colin Nish headed on a Peter Leven corner and Steven Naismith's head flick brought a fine one-handed save from Andy McNeil.
It was an open Final and Lewis Stevenson had a chance at the other end after a throw-in from David Murphy but Alan Combe leapt to his left to beat out his shot.
Ivan Sproule caused Kilmarnock problems with his pace on the right but too often the winger's final pass let him down.
Kilmarnock had to be content with chances on the break and Naismith hooked a shot narrowly wide after he got in behind the Hibs defence.
Hibs took the lead after 28 minutes when Jones powered home a header from close range from a Murphy corner.
Hibs dominated the rest of the first half and Combe had to scramble across his goal to keep out a Fletcher header.
McNeil did well at the other end to react quickly to hold a shot from Frazer Wright after the Kilmarnock player's initial free-kick broke back off the defensive wall.
But Hibs should have been two ahead on the stroke of half-time when Benjelloun's 10-yard shot struck Sproule just a yard out.
Fletcher missed a great chance after 57 minutes when he curled his shot wide after Guillaume Beuzelin had set him up.
But the goal was only delayed a couple of minutes. Steven Whittaker released Benjelloun and he teased the Kilmarnock defence before curling home a left-foot shot.
Fletcher scored the third after 66 minutes when he beat the offside trap before tucking a left-foot shot past a stranded Combe.
Gordon Greer headed a late consolation for Kilmarnock when Hibs failed to deal with substitute Gary Locke's cross.
Benjelloun added his second five minutes from time with a slick finish with his right foot and a dreadful mistake by Combe presented Fletcher with his second a couple of minutes later.
Benjelloun was denied a hat-trick right at the death when his header struck a post.