Leicester were given a fright when Blackpool levelled midway through the second half before Mark De Vries settled their nerves with his second strike of the night to guide City safely through to the next round.
For most Leicester fans this may have been an unattractive fixture, but history was made in the final minute when Ashley Chambers replaced Momo Sylla to become the Foxes youngest ever player.
Aged just 15 years and 122 days, Chambers beat the previous record held by David Buchanan who made his debut when aged 16 years and 192 days at home to Oldham Athletic in January 1979.
Early on Elvis Hammond twice tested the Blackpool keeper before Alan Sheehan fired in a 25-yard free-kick which Les Pogliacomi was grateful to punch away.
The Seasiders were constantly stretched by Leicester's pace and they were undone on 17 minutes when De Vries gave the Foxes the lead.
Hammond surged towards goal with Pogliacomi dashing from his line to tackle the speeding forward. But the loose ball fell to De Vries who hoisted it over the back-peddling keeper and into the back of the net from 20 yards.
On 24 minutes Joey Gudjonsson's 20-yard free-kick was pushed away by the overworked Pogliacomi, but De Vries wasn't quick enough to take advantage.
And on 30 minutes the same player was again denied, this time with the keeper turning his 12-yard shot away for a corner.
It continued to be one-way traffic towards the Blackpool goal after the break, but despite their domination City struggled to find the second goal which would have put them in the comfort zone.
Blackpool worked hard to keep the Foxes at bay, and their persistence was rewarded on 68 minutes when Keigan Parker - a half-time substitute for Scott Vernon - ran on to a Ciaran Donnelly throughball and held off a defender before shooting beyond Paul Henderson from 12 yards.
But Leicester restored their narrow lead on 77 minutes when Pogliacomi blotted his copy book when he failed to hold a Sylla corner and De Vries pounced to hook home the ball from close range.