Darren Moore’s men were put to the sword as Jaden Brown’s own goal was sandwiched between Mark Shelton’s header and Will Goodwin’s effort.
Moore named a much-changed side as he rested a whole host of first-team regulars against the League Two outfit.
There was a scrappy start to proceedings in South Yorkshire, but the visitors burst ahead after just 11 minutes as Shelton rose highest to nod home the opener.
And within a flash the tie was all but done as a mix-up between Brown and goalkeeper Joe Wildsmith resulted in a comical own goal in the 15th minute as the defender’s attempted pass back from the left flank ended up in his own net.
Wildsmith kept the deficit at just the two with a low save from Joe Grey’s tame effort. Martin Smith should have made it three for the visitors after Sylla Sow was caught in possession.
Defender Ciaran Brennan went close to pulling one back as he agonisingly missed the target.
The hosts made a triple change at the break in a desperate bid to get back into the game.
But the Pools added another as Goodwin nipped in at a corner.
Sheffield Wednesday: Wildsmith; Paterson, Brennan (Adedoyin, 84), Brown; Corbeanu, Wing (Agbontohoma, 69), Dele-Bashiru, Byers (Hunt, 45), Shodipo (Bannan, 45); Berahino, Sow (Windass, 45). Unused substiyutes: Render, Waldock, Bannan.
Hartlepool: Mitchell, Sterry, Odusina, Hendrie, Francis-Angol (Byrne, 84), Jones, Smith, Crawford, Shelton, Goodwin (Fondop, 84), Grey (Olomola, 80). Unused substiyutes: Killip, Ogle, Ferguson, Holohan.
Referee: A Haines (Tyne & Wear)