The two sides now face a replay at the Withdean Stadium with Loft's goal having cancelled out a 77th minute Steven Gillespie strike that looked to have sent the home team through.
New Cheltenham boss Keith Downing thought he had bagged his first victory as the club's permanent manager, only for Loft to spoil his celebrations when he swept in a shot left-footed from the edge of the box after Bas Savage had produced a strong run and cross from the left.
Brighton certainly deserved a draw having created the better chances in a drab match that only got going in the last 15 minutes.
The visitors were slicker of movement and more careful in their passing, although Cheltenham worked and chased as if their lives depended on it.
Town goalkeeper Shane Higgs made first-half saves from Dean Cox and Jake Robinson, while Brighton striker Nicky Forster should have done better with a close-range header from a Savage cross that he sent over the crossbar.
Higgs also saved well from defender Adam El-Abd and Cheltenham defender Jerry Gill cleared off the line from Savage; but the home side stuck to their task and grabbed the lead from a free-kick 13 minutes from time.
Midfielder David Bird curled it to the far post where Steven Gillespie was lurking to poke a shot under goalkeeper Michel Kuipers.
Substitute Nathan Elder almost levelled for Brighton four minutes from time when he shot wide at the far post, but it was Loft who took the adulation of the travelling fans seconds before the time added board was raised by the fourth official.