Bury played their part in a close contest but found little going right in front of goal.
Robbie Weir tested Bury goalkeeper Cameron Belford inside the first minute with a well struck shot.
The visitors could not capitalise on some good approach work and the Merseysiders were ahead in the 24th minute. Labadie netted with a low shot just inside the box after Lucas Akins stepped over a Jose Baxter corner.
It needed a terrific reaction save from Belford to keep out a Baxter strike which took a big deflection off Mark Carrington approaching the hour and soon after Belford was tested again by Baxter.
Bury upped the ante and Mark Hughes and sub Ashley Eastham were very unlucky to shave the bar with headers from crosses by Mike Jones on 77 minutes and 87 minutes. Tranmere made sure when Taylor turned in a Zoumana Bakayogo pass in the 90th minute.