Skipper Dean Hammond hit a dramatic late penalty as Brighton clinched their third successive home win. Hammond had put the Seagulls ahead 11 minutes after the break by heading in a corner from Kerry Mayo.
But substitute Jamie Victory put Cheltenham on course for their first league draw of the season with a low shot off the post 16 minutes from time.
But Hammond kept his cool to net from the spot a minute from time after Gavin Caines had hauled down Alex Revell.
Brighton: Henderson, Whing, Adam Hinshelwood (Hart 80), Lynch, Rents, Fraser (John 61), Hammond, Mayo, Cox, Revell, Robinson.
Subs Not Used: Kuipers, Gatting, Santos.
Booked: Mayo, Henderson, Hart.
Goals: Hammond 56, 89 pen.
Cheltenham: Higgs, Wilson, Caines, Duff, Armstrong, Melligan, O'Leary, Finnigan (Victory 69), Bird (Yao 69), Spencer, Odejayi.
Subs Not Used: Guinan, Brown, Townsend.
Booked: Duff.
Goals: Victory 74.
Att: 5,386
Ref: J Singh (Middlesex).