Gary Baker put the Blues ahead with a well-worked goal midway through the first half with Bury equalising before the break to send the teams in level at half-time.
The Shakers went ahead shortly after the break with a goal from a corner, only for 2nd year-YTS midfielder James Earl to restore parity to the scoreline at 2-2.
Bury took the lead again in an end-to-end physical encounter with a short-range effort after some poor defending by the United youngsters. Shaun Vipond then kept the scorers busy by smashing home a fantastic 30-yard drive to pull United back level leading boss Wilkes to make a couple of late substitutions as Carlisle went for the win.
United's attacking play was rewarded in the 80th minute when schoolboy signing Mike Stewartson knocked the ball home following a parried save by the Bury keeper to give the Blues all three points in a keenly contested 4-3 victory.
United line-up :
Adam Bradley, Richard Hoban, Matthew Blake, Matty Bell, Dan Kirkup, Gary Baker, James Earl, Shaun Vipond, Andy Hardman, Rob Bainbridge, Paul Gardiner.
Subs (both used) : Ashley Combe and Mike Stewartson.
Official site report :
http://www.carlisleunited.premiumtv.co.uk/page/News/NewsDetail/0,,10361~703029,00.html