Yves Bissouma broke the deadlock in spectacular style, finding the top left corner from 30 yards out.
It was a deserved goal for Albion, who dominated proceedings in the first half.
However, Blackpool pulled themselves level right before the half-time whistle, with the experienced Gary Medine finishing off a well crafted goal.
Brighton restored their lead shortly before the hour mark in fortunate fashion — Alexis Mac Allister's strike found the net via a deflection off Steven Alzate's back.
The Seagulls wasted plenty of chances to put the game to bed but held on to their slender lead to progress to the next round.
Scroll down and click through to see how journalism student Sam Cox rated Graham Potter's side out of ten.
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1. Christian Walton - 8
The 2018 FA Cup quarter-finalist with Wigan Athletic didn’t have a great deal to contend with across 90 minutes. Walton made a great acrobatic save to deny Luke Garbutt’s free-kick, and had little chance of saving Madine’s close-range equaliser.
2. Dan Burn - 7
Another member of a solid defensive backline display. Burn never looked uncomfortable, on or off the ball, and was rarely tested.
3. Lewis Dunk - 7
Another consistent and comfortable afternoon for Albion’s captain. Will be frustrated by Blackpool’s equaliser in first half injury-time, but was rarely tested throughout.
4. Adam Webster - 7
Looked dangerous from set-pieces throughout and couldn’t be faulted for Blackpool’s equaliser. The former Bristol City defender picked up a nasty looking cut above his eyebrow early in the second half but soldiered on.