The Championship side were leading through a second senior goal from 17-year-old midfielder Jake Forster-Caskey, but Polish striker Cieslewicz grabbed an equaliser in front of 2,000 delirious travelling fans.
There was certainly a whiff of an upset in the air on the south coast, 20 years to the weekend since the most famous day in Wrexham's history, namely the 2-1 win over then champions Arsenal at the Racecourse Ground.
The Dragons are currently flying high at the top of the Blue Square Bet Premier while Brighton were riddled with injuries and suspensions.
And although they could not quite repeat the 1992 heroics of Mickey Thomas and company, Wrexham will still fancy their chances of a place in round four when they take Brighton back to Wales.
As well as giving Forster-Caskey only his second senior start, Seagulls boss Gus Poyet was forced to hand full debuts to fellow youngsters Grant Hall and Ben Sampayo in his back four.
Nevertheless, the hosts started on the front foot with Kazenga LuaLua a lively presence in attack, the former Newcastle winger twice darting inside and unleashing fierce drives which flew narrowly wide.
Will Buckley also had a shot blocked and long-range efforts from Alan Navarro and Forster-Caskey were held by Wrexham goalkeeper Joslain Mayebi.
But the Seagulls were indebted to Matt Sparrow for a last-ditch tackle to deny Jake Speight from player-boss Andy Morrell's cross.
Moments later Jamie Tolley had a great chance for the non-leaguers when he met Speight's cross 15 yards out but he put his shot wide.
Albion keeper Peter Brezovan then did well to keep out a 20-yard effort from Tolley with Speight unable to latch onto the rebound as the first half ended goalless.
But the deadlock was broken just 90 seconds after the restart with LuaLua the catalyst.
He charged down the left wing and sent in a precise cross which Forster-Caskey was able to tap in from a couple of yards out.
Sadly for Brighton, LuaLua's afternoon did not last much longer after he pulled up with a hamstring injury and had to be substituted.
Forster-Caskey came close to a second with a ferocious, swerving shot which Mayebi did well to hold onto.
But instead the Wrexham fans who had packed out the south stand at the Amex Stadium were celebrating in the 62nd minute when Cieslewicz went on a mazy run into the area before giving Brezovan no chance with a shot from 15 yards.
Brighton substitutes Anton Rodgers and Torbjorn Agdestein had chances to put them ahead again but narrowly missed the target, while Brezovan saved from Tolley in stoppage time to deny Wrexham another cup scalp - for now at least.
