Once again Leek's management team of Jamie Cullerton and Simon Bell shuffled the pack with another trialist featuring in defence.
Blues got off to a poor start and the Bears went 2-0 up through goals from Youssef Abdullahi and Jason Carey.
However Town pulled a goal back shortly before half-time with a penalty from Jonny Higham and then managed to equalise before the break through a header by Sam Grimshaw.
Congleton went back in front on 63 minutes thanks to Damani Holness and made it 4-2 when Derek Fletcher scored in the 81st minute.
Substitute Tim Grice pulled a goal back a minute later, but Leek were unable to force an equaliser.
Team: Jaaskelainen, Faulkner, Morris, Beaumont, Trialist, Kearns, Shelley, Grocott, Higham, Stevenson, Grimshaw
Subs: Chadwick, Curley, Maguire, Johnson, Green, Grice, Wyatt