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The teams were tied at 2-2 after extra time, but Blackpool clinched a place in the third round when skipper Michael Jackson tucked away his spot-kick to give the visitors a Premiership scalp.
Derby had twice been in front through goals by Mo Camara and Craig Fagan, only for Latvian defender Kaspars Gorkss to peg them back with powerful headers.
But Blackpool deserved to take the match into extra-time and arguably they should have sealed in the contest in normal time but for wayward finishing.
Derby goalkeeper Stephen Bywater was the busier and made several vital saves as Blackpool threatened to embarrass the home side.
Although Derby had made seven changes, Blackpool had also rested seven players and shaded a disappointing first half in which both teams failed to take a grip of the match.
Keigan Parker had the best chance before the break and he had another opportunity in the 56th minute when Scott Vernon put him clear, but Bywater just did enough to turn the ball around a post.
Parker then struck the outside of the right post with a shot from just outside the area, but Derby took the lead in fortuitous circumstances in 63rd minute when Camara's intended cross from the right crept inside the right-hand post for his first goal in nearly three years.
Blackpool fought back and drew level in the 86th minute when Shaun Barker crossed and Gorkss climbed above everyone at the back post to head into the top corner.
Derby regained the lead 11 minutes into extra-time when Fagan was left unmarked to head in a Gary Teale cross, but Gorkss again levelled in the final minute from another right-wing cross.
Both teams missed two penalties to take the shootout into sudden death but defender Darren Moore put his kick wide of the post to leave Jackson with the chance to give Blackpool a memorable victory.