The former Gillingham man connected with a Gary Dicker corner on 77 minutes to seal the win for the Seagulls at the expense of the hosts, who were bidding to reach the fourth round for the second season in a row.
After a ten-minute delay to the start of the proceedings, the Gulls were on top early on but found the Brighton defence difficult to break down.
In the 13th minute, Torquay launched a counter attack with winger Jake Thomson made a bursting run from inside the Gulls half of the pitch.
He then delivered a cross from the right wing which found Elliott Benyon, whose 25-yard effort was collected comfortably by Brighton keeper Michel Kuipers.
Torquay were defying the gap of 23 league places separating the two sides as Wayne Carlisle fired a 20-yard effort wide on 22 minutes.
Defender Kieran Charnock nearly opened the scoring for Torquay when he connected with a Thomson cross to force a fine, finger-tip save from Kuipers with a headed effort on 26 minutes.
Brighton enjoyed more of the possession as the half wore but were unable to create many clear cut chances.
The pick of their efforts fell to Glenn Murray in the 43rd minute but his close-range shot was saved by Michael Poke.
The first chance of the second half fell to Seagulls defender Adam Virgo, who fired over the cross bar for the visitors on 49 minutes.
In the 51st minute, Benyon headed a cross from right-back Lee Mansell back across goal and straight into the arms of Kuipers.
But Brighton finally scored the decisive goal of the afternoon on 77 minutes when Crofts broke clear of Gulls skipper Chris Hargreaves to head home Dicker's corner.
Kevin Nicholson tested Kuipers in the dying minutes with a free-kick for Torquay, but the Seagulls were able to hang on to secure their passage into the fourth round.