Stoke City
On The Bench
Preston
On The Bench
The towering centre-back headed home in either half to take his tally to six since joining the Potters in November from Crystal Palace, initially on loan, before making the move permanent this month.
Cort's goals sandwiched a 28th-minute strike from Richard Cresswell and although Chris Brown struck in the second half to give Preston hope, Stoke ultimately took an easy win.
It was the perfect way for Tony Pulis' men to bounce back from their crushing FA Cup exit at Newcastle in midweek.
The Potters were unrecognisable from the side which surrendered meekly to a 4-1 defeat at St James' Park and dominated Alan Irvine's side from the outset.
North End, struggling desperately at the wrong end of the table, simply failed to cope with Stoke's aggressive physical approach and were up against it from the first whistle.
Cort's 16th-minute opener was indicative of Stoke's control and was fashioned by midfielder Rory Delap.
The former Southampton man swung in a dangerous cross from the left flank and Cort rose highest to plant a firm header past Andy Lonergan.
Preston sought to find an immediate response but playmaker Paul McKenna saw his shot superbly blocked by Ryan Shawcross and Stoke survived.
And in the 28th minute it was 2-0 courtesy of a dreadful error from North End stopper Lonergan.
Liam Lawrence swung in a harmless-looking cross but Lonergan fumbled the ball badly and Cresswell lashed in the loose ball from six yards.
Preston's highly-rated midfielder Simon Whaley then warmed Steve Simonsen's hands from 25 yards but it was a routine save and Danny Pugh came close to adding a third for Stoke with a volley from distance.
Shawcross also tried his luck from distance as Stoke failed to add to their tally before the break.
Preston's initial response after the break was encouraging and McKenna's whipped cross in the 57th minute deserved better than a wayward header from Brown which flew over the crossbar.
Five minutes later, Lawrence narrowly missed the target from 25 yards but in the 68th minute Preston pulled a goal back.
Lewis Neal headed the ball into the danger zone and Brown stooped to nod it into the back of the net from six yards.
That encouraged hopes of a Preston fightback but Cort soon put paid to that by netting his second four minutes later.
Lawrence swung in a corner from the right and Cort was again afforded the time and space to head the ball home from 12 yards.
North End came close to finding an almost immediate reply when Darren Carter drilled wide from 25 yards.
But it could have been worse for the visitors in the closing stages as Pugh produced a left-footed strike which drew a smart stop from Lonergan.
