Rekeil, Duane Holmes and William Boyle scored as Huddersfield Town Under 21s made it four wins on the trot.
They were 3-0 victors at Crewe Alexandra in the Professional Development League.
Sondre Tronstad set up Pyke for a 27th-minute opener.
Holmes beat the Crewe keeper in a one-on-one seven minutes into the second half.
And Boyle converted from a close range after a Jack Boyle cross was spilled after 75 minutes.
Town: Wilczynski; Senior, W Boyle, Kane (Horsfall, 80), Hanson; Booty, Billing, Tronstad, D Holmes; Pyke (B Holmes, HT), Coughlan (J Boyle, 68).
Unused subs: Guthrie, Wilkinson.