Lee Casswell made one change to his starting line-up from the side that played at Carlton Town with Christian Millar replacing Matt Bradbury.
Matt Haddrell also made the expected move to the back to man mark Ilkeston's Gary Ricketts.
Blues were under pressure from the off and with a strong wind against were struggling to get out of their own half for much of the first period.
A combination of some excellent defending and wayward shooting meant much of Ilkeston's threat was confined to long range efforts, many of which troubled the car park rather than Ben Chapman.
However Chapman did have quite of number of crosses to deal with as The Robins racked up the corner count in the opening 45 minutes.
Leek's only effort of note was a shot grom Tim Grice after 10 minutes that went over the bar.
Blues tactics of frustrating Ilkeston seemed to be working as they enjoyed a little more possession after the break, but the home side did finally force Chapman into a good save after 53 minutes.
The goal finally came on 70 minutes when Ricketts set up Matt Richards who fired home with a low shot that went in off the inside of the post.
Two minutes later, The Robins doubled their advanteage when Daryl Thomas hit a fierce shot from the edge of the area which seemed to swerve at the last moment and deceived Chapman.
Shortly afterwards, Ricketts thumped a header against the crossbar as Ilkeston threatened to run riot against a visibly tiring Blues side.
With five minutes remaining, Leek finally got their first effort on target when substitute Aden Johnson fizzed a 25 yarder goalwards which the keeper tipped round the post.
Christian Millar got his head to the resulting corner, but his effort went over the bar and Blues knew the game was up.
In the final analysis, the home side looked sharper and quicker all through the game. Blues having played extra-time on Wednesday and had two days less rest than Ilkeston and simply found this one match too many.
Team:
1. Ben Chapman
2. Tim Sanders
3. Matt Bell
4. Jon Guthrie
5. Anthony Danylyk
6. Christian Millar
7. Tim Grice (12. Oliver Edwards, 76)
8. Ricky Bridge (15. Aden Johnson, 65)
9. Matt Haddrell
10. Dan Cope (17. Jamie Pointon, 58)
11. Ashley Woolliscroft
Unused Subs: 14. Matt Bradbury, 16. James Brough
Cards: None
Attendance: 1670