Ishmel Demontagnac, Ben Burgess and Charlie Adam were on target to put the tie beyond doubt after just 33 minutes.
Ishmel: Quick off the mark for Blackpool
It could hardly be called a giant-killing by the Championship side. Wigan fielded only two of the men who started their 5-0 defeat by Manchester United on Saturday.
Blackpool, who drew their first four League games and won at Crewe earlier in the Carling Cup, had only four starters from their weekend draw at Watford.
Ishmel, the midfielder conveniently known by his first name, was on target just three minutes into his first start for Blackpool. The 21-year-old, signed on a free transfer from Walsall, had been restricted to an hour of action in three appearances as a substitute, but he was sharp enough when he moved on to a square pass from Burgess and hit a fine low shot to beat Mike Pollitt's despairing dive.
There was briefly a threat from the visitors after 11 minutes when Ben Watson's driven free-kick was beaten clear, but after 19 minutes it was 2-0 with striker Burgess applying the finish in similar fashion to Ishmel, with Pollitt again beaten as he dived to his left.
It got worse for the Premier League men, with Adam shooting Blackpool's third after 33 minutes, firing in the rebound after Pollitt had saved his penalty, awarded for a foul by Paul Scharner on forward Billy Clarke.
Martinez could not have expected anything like this, even when giving his fringe players a chance, employing only Scharner and recent signing Mohamed Diame of Saturday's starters at the kick-off.
But this season is turning into a nightmare for the Spaniard despite the dream opening to his time in charge of victory at Aston Villa in the opening-day Premier League fixture.
Since then there have been home defeats by Wolves and the side who hold the Carling Cup and also the title. Now this, and to make it worse he had to watch players he will often call on in the top division, even if not regularly, taken apart by opposition also loaded with second-choice players and still to record a win in the Championship.
Scott Sinclair promised to provide hope of a revival four minutes into the second half but his free-kick was pushed aside by the diving Matt Gilks. Blackpool fans gave Ishmel a standing ovation when he limped off after 53 minutes.
Gary Taylor-Fletcher, a regular starter but only used as a substitute here, made it 4-0 with a low shot into the far corner after 66 minutes.
Antonio Amaya's header in the closing seconds was scant consolation for woeful Wigan.
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