After a goalless first half, the second period proved more entertaining with opportunities to score coming at both ends.
Lewis Collins, who impressed in midfield, shot narrowly wide after good work by Jack Walters and Luke Lofts.
Blyth then had a 10-minute dominant spell, although only one clear-cut chance came their way when Jarrett Rivers forced Ross Durrant into making a smart, one-handed save.
Lofts had a shot blocked before the game’s only goal arrived on 60 minutes, Cooke heading home Jamie Forrester’s nicely-flighted free-kick.
Despite Blyth pressure, Ferriby held on and could have actually doubled the score only for goalkeeper Peter Jameson to deny Collins as he burst through.
“This win was fully deserved,” said Ferriby manager Chris Bolder afterwards.
“We know we may have to surrender possession and territory at times during games. I felt they got a bit desperate at times and they found us hard to break down because we defended so well.
“It was nice for the fans to see a home victory.
“Those who have been coming recently will have seen this result coming. We’re in good form given that we are in a rebuilding process.”
First-half dismissals for Matt Hill and Oli Johnson completed an awful opening 45 minutes for Bradford Park Avenue at FC United, as they went down 4-0.
The Yorkshire club were further hampered when injured pair Ryan Toulson and Adam Boyes also left the action before the break.
FC United capitalised fully with Jeff King scoring from two free-kicks and then adding a penalty after Gerard Garner had got in on the act from close range.