Blackpool never looked back after taking the lead after three minutes through Ishmel Demontagnac.
They were 3-0 ahead at half-time with Ben Burgess and Charlie Adam also on target. Substitute Gary Taylor-Fletcher grabbed a fourth in the second period.
Martinez made nine changes to his side but Demontagnac made the breakthrough when he thumped a shot beyond goalkeeper Mike Pollitt from the edge of the box.
It was Demontagnac's first goal for Blackpool since he arrived at Bloomfield Road eager to get his career back on track.
The 21-year-old was sacked by Walsall last November after a series of misdemeanours which infuriated club officials.
This was his first start for the club after three substitute appearances. He was called up after playing for the reserves on Monday.
Blackpool extended their lead in the 19th minute with Pollitt looking at fault.
He was slow to react as Burgess drilled in a shot from the edge of the area that did not have much power.
Pollitt, though, allowed the ball to drift past him into the corner, leaving Wigan with an uphill task.
Blackpool were looking comfortable and Stephen Crainey tested Pollitt in the 29th minute with an inswinging free-kick.
Wigan responded and Scott Sinclair saw his shot beaten away by goalkeeper Matt Gilks.
It was a brief respite for the Premier League side as Demontagnac unleashed another thunderbolt that Pollitt did well to block.
Blackpool then made it 3-0 in the 33rd minute with Wigan all at sea at the back.
Paul Scharner conceded a penalty after flooring Billy Clarke as he homed in on goal.
Charlie Adam stepped up and although Pollitt got a hand to his effort, he was unable to prevent him scoring from the rebound.
Wigan almost pulled a goal back in the 48th minute when Scott Sinclair's free-kick evaded the wall only for Gilks to make a superb block.
Gilks again reacted quickly moments later to push away Ben Watson's effort before Blackpool made it 4-0 in the 66th minute with a marvellous strike from Taylor-Fletcher.
There seemed little on when he picked the ball up but he weaved his way into the area before finding the corner.
Ormerod almost added a fifth goal in the 84th minute only for Pollitt to take the ball off his feet as Blackpool secured their place in the third round with ease.
Wigan grabbed a consolation goal in stoppage time when Antonio Amaya marked his debut by heading in Ben Watson's corner.