Struggling Stockport County's winless run was extended to nine league games, as Phil Bolland's header handed Barrow three points.
Sean McConville tested home keeper Danny Hurst's reactions early on.
Visiting custodian Matt Glennon was forced into fine saves by Paul Rutherford and Andy Cook before Bolland headed home from Richie Baker's corner.
Hurst then saved well from Ryan Fraughan and Danny Rowe as the Hatters searched in vain for a leveller.
The Hatters have now gone 481 minutes without a goal.