The 21-year-old, signed on loan from Ipswich this week, scored the fastest ever debut goal by a Northampton player when he fired them in front inside two minutes on the way to a memorable hat-trick - the first by a Cobblers debutant in nearly 50 years.
His opener could have come a few seconds earlier as his first effort was weak, only for the ball to bounce luckily back into his path, allowing a no-nonsense finish.
Crewe's recent revival under new boss Gudjon Thordarson was held in check and the dismissal of skipper Julien Baudet after 17 minutes for a trip on Giles Coke virtually ended their chances, especially when Danny Jackman curled the free-kick home for the second.
Crewe pulled a goal back ten minutes later when Mark Carrington's cross from the right was stabbed home by Colin Daniel and the visitors briefly threatened a revival.
Clarke had scored four goals in one game while on loan at Darlington earlier this season and his early success clearly whetted his appetite as he headed in his second in the 56th minute, after Jackman's cross was nodded back across goal by Adebayo Akinfenwa.
Within a minute Liam Davis had made it 4-1 with a terrific left-foot strike from the edge of the box, rifled low into the far corner.
It could have been worse for Crewe as Giles Coke then headed a cross by Leon Constantine wide of the target, but Clarke completed his treble in the 69th minute from the penalty spot.
Referee Steve Cook pointed to the spot after Clarke was tripped in the box as he raced clear on to a pass by Akinfenwa, only being halted by Daniel.
Akinfenwa, Northampton's top scorer and regular penalty taker, sportingly stood aside to allow Clarke to complete his red letter day.