The striker, currently on loan from Chippenham, but due to sign on a permanent basis, spared Walsall's blushes after Pool had dominated the first half.
Just two minutes after the restart Constable produced a fine running header to beat keeper Lee Jones from a free-kick by Simon Osborn.
Walsall were immediately lifted and five minutes later a low cross by Mark Wright was half cleared and Constable seized the chance to drive home low from the edge of the box.
It was a turnaround because the Seasiders had dominated the first period, without ever looking dangerous. In fact the best chances fell to Walsall striker Jorge Leitao, playing his last home game for the club before returning to Portugal in nine days' time.
The first came on 23 minutes when he raced on to a Constable pass only to fire straight at Jones.
Five minutes before the break a cross by Wright found Leitao racing in but his downward header was cleared for a corner.
Although having a lot of the territorial advantage the best Blackpool could muster was a shot by John Doolan on 26 minutes which flew over.
With central defenders Anthony Gerrard in particular and Ian Roper a pillar of strength for Paul Merson's men, Blackpool scarcely had a shot in the second half, although a tremendous 30-yard drive by Keith Southern was superbly tipped over by Joe Murphy.
Walsall, without ever playing well, picked up another useful three points despite having to play much of the match without leading marksman Matty Fryatt, who went off with a hamstring injury on ten minutes.
But with subs like Constable around the Saddlers are always capable of scoring at home.