Striker James Hanson gave the Bantams victory with a 32nd-minute header.
The striker had a stroke of luck as Kieran Charnock's clearance rebounded off Gareth Evans and looped perfectly into the path of Hanson who headed past the helpless Joe Anyon from six yards out.
They should have extended their lead five minutes into injury time when Kevin Ellison won a penalty after being brought down by Andy Parrish but Gareth Evans saw his spot kick saved by Anyon.
It was Jackson's side who had the better of the chances throughout with Morecambe keeper Anyon making excellent saves from Gareth Evans and Michael Flynn to keep the scoreline down.
Morecambe threatened rarely. Moments after Hanson's opener Garry Hunter missed the target from six yards out from Laurence Wilson's cross when he looked certain to score and in the closing minutes Stewart Drummond headed a Chris Shuker cross weakly at John McLaughlin.
Source: PA
Source: PA