Although they dominated the first half, City fell behind in the 41st minute when they failed to clear a long throw-in and David Goodwillie scored from close range.
But the Foxes stormed to their 25th win of the season with second-half goals from Riyad Mahrez, Wes Morgan and substitute Kevin Phillips to take another big step towards promotion.
It was their fourth win in a row and took them 17 points clear of Derby in third place.
Leicester were unchanged after the midweek win at Barnsley while Blackpool brought back Jack Robinson, with Ricardo Fuller dropping to the bench.
Having beaten Millwall on Tuesday for their first win in 18 league games, Blackpool came into this daunting fixture against the leaders in good heart.
But they were soon on the back foot as the Foxes launched a wave of early attacks. Mahrez fired just wide after a Matty James shot had been blocked and Anthony Knockaert put another chance into the side-netting from a Jeff Schlupp pass.
The pressure continued with Vardy heading wide and David Nugent just off target with an angled shot from the right of goal.
Then, in the eighth minute, a neat touch from Nugent sent Vardy clear and he beat the advancing Matt Gilks with ease, but the celebrations were cut short by an offside flag.
There was another scare for Blackpool two minutes later. Mahrez finished off a long run from inside his own half with a right-foot shot that almost squirmed out of Gilks' hands and over the line.
But it was Blackpool who squandered the best chance so far in the 17th minute, when Neal Bishop put a free header wide at the far post from Andy Halliday's corner.
It was still all City though, and in the in-form Vardy, who has scored five goals in the last four games, incredibly missed two gilt-edged chances in the space of six minutes.
In the 31st minute Danny Drinkwater sent Ritchie De Laet racing down the right with a brilliant pass and the right-back responded with an equally impressive centre. Vardy met it on the volley but somehow put his shot just wide from inside the six-yard box.
Then he was sent clear with a magnificent ball from Mahrez, but this time dragged a right-foot shot just wide of the far post.
The Foxes paid dearly for the misses as Blackpool grabbed a shock lead in the 41st minute. A long throw in by Robinson caused confusion, with Kasper Schmeichel failing to clear with an intended punch, and the ball fell to Goodwillie, who chested the ball down and volleyed home from close range.
There was little doubt that the goal was a real shock to the system for City, but they hit back hard at the start of the second half with Mahrez playing Nugent through with another fine pass. However, Nugent was crowded out before he could get in a shot.
Then in the 60th minute the impressive Mahrez equalised with a stunning strike.
Picking up the ball out on the left he cut inside and scored with a swerving shot from 20 yards that left Gilks clutching thin air. A few minutes later Mahrez picked out Nugent with an inch-perfect cross, but the striker's header was brilliantly saved by Gilks.
City stepped up the pace in search of a winner and substitute Gary Taylor-Fletcher almost scored against his former side with a shot that scraped past the far post.
But the Foxes were not to be denied and Mahrez produced another superb cross in the 82nd minute which Wes Morgan headed home at the far post.
And in the 87th minute substitute Kevin Phillips sealed victory with a shot into the roof of the net from a Drinkwater cross.