Knight kept his cool to beat City goalkeeper Steve Phillips from the spot after Danny Coles brought down Chris Iwelumo to clinch victory in a tense encounter.
A tentative first half saw little in the way of goalmouth action, as the two well-organised defences dominated proceedings.
The first shot on target came after 11 minutes when the Robins' veteran midfielder Brian Tinnion saw his free-kick saved by Ben Roberts.
Five minutes later Seagulls keeper Roberts failed to deal with a Craig Woodman cross and was relieved to see Tony Rougier's shot from the rebound blocked.
The best chance of the half fell to Brighton shortly before the interval, but Knight saw his free-kick strike the crossbar and rebound to safety.
The game did not improve much after the break, with both sides seemingly more interested in avoiding conceding a goal than finding a winner.
What little attacking intent there was came from Danny Wilson's side, with captain Tommy Doherty increasingly influential.
However, Albion's prolific front pair of Knight and Chris Iwelumo began to make their mark on the game in the closing stages.
Iwelumo was twice presented with clear openings, but shot weakly from distance before heading John Piercey's cross wide.
Then came the game's crucial moment, Coles mis-timing an attempted clearance and inadvertently bringing down Iwelumo - leaving Knight to slot home the spot-kick.
It left Albion with six minutes plus added time to hold on to their slender lead, which they did successfully thanks to the outstanding centre-back partnership of Guy Butters and Danny Cullip.