The visitors opened the scoring when, on the back of a penalty, Luke Ambler and Scott Murrell combined to send in Ross Divorty.
The home side then piled the pressure on the Halifax line. However, they failed to turn that pressure into points and the visitors made them pay. Divorty went from scorer to provider, as he fed Ryan Fieldhouse through to the line, Tyrer making no mistake with the boot to send them further clear.
Keighley hit back after former Halifax scrum-half Paul Handforth’s scuffed grubber was picked up by Jode Sherrife, who powered his way through to the line.
Halifax then shot out of the blocks after the break. In the first set, Tommy Saxton’s break downfield laid the platform for Dane Manning to cross on the next tackle.
It was not long after that Cougars replied, though, with Danny Jones’s cut-out pass playing in James Haley back on the inside and through to the line.
All the momentum was now with the home side, as James Feather then scooted his way over from dummy half. But Jones missed the crucial conversion that would have drawn them level.
The visitors then quickly went on to extend their lead to eight points through Luke Ambler and the back of Scott Murrell’s offload, with Tyrer making no mistake with the booted conversion.
Paul Mennell then cruelly took the bonus point away from Keighley in the final minute, as he side-stepped and left Josh Lynam in his wake to cap off the victory before Tyrer rounded off the scoring.
Keighley Cougars: Jesse Sheriffe; Barnett, Lawton, Haley, White; Jones, Handforth; Shickell, Feather, Hesketh, Lynam, Rawlins, Lindsay. Substitutes: Jode Sheriffe, Sagar, Cherryholme, Haigh.
Halifax: Fieldhouse; Fox, Manning, Tyrer, Saxton; Murrell Johnston; Tonks, Kaye, Ambler, Bracek, Divorty, Adamson. Substitutes: Mennell, Davies, Casey, Spencer.
Referee: C Kendall (RFL).