The goal ended the Foxes' recent four-game unbeaten run, while for Blackpool it was their first win in five.
The home side had been given a dream start when Gary Taylor-Fletcher curled home a clever finish in the third minute for his third goal of the season.
The Seasiders dominated the first half but Ben Burgess fired wide when put through and Shaun Barker headed over from eight yards just before the break.
However, the visitors came out fighting after the break and, after one of their new signings Steven Howard had flashed his header wide just minutes after the restart, the former Derby Country frontman slotted home his second goal for his new side just after the hour mark.
Ex-Foxes player and current Blackpool boss Simon Grayson was obviously delighted with the precious win but conceded that neither side deserved the three points.
"There were dreadful conditions but the three points are the main thing. We didn't play too well but it's all about results," he said.
"It was a tale of two halves. Neither team deserved to win but we never gave up and Dickov will always give you a chance around the box.
"He's a player I've trailed for six months and you know what you're getting with him."
Leicester boss Ian Holloway was disgusted with his side's performance, saying: "In the first half we deserved nothing, we looked like a team playing a lesser team in the FA Cup.
"They had two shots and scored two goals. It was absolute schoolboy defending on our part.
"After the break, however, we did improve and I'm bitterly disappointed we didn't get something from the game.
"We need to dust ourselves down and realise where we are, we're in a scrap.
"I'm sick and fed up, it's one step forward and two back. We haven't won back-to-back games all season which is a disgrace for a club like Leicester City."