Rangers appeared to have the game in the bag at one stage as they closed in on half time with a two-goal lead, but a surprise riposte seconds before the break set up a tense second 45 minutes.
The biggest home crowd of the season was briefly silenced six minutes into the game when Brighton's Charlie Oatway's goalbound volley from the edge of the area was blocked on the line by Clarke Carlisle.
Rangers' Martin Rowlands and Brighton's Leon Knight came close to breaking the deadlock before the opening strike on 20 minutes.
Rowlands advanced up-field when offered time and space by the visiting defence before unleashing a superb low curler beyond the dive of Ben Roberts.
The hosts failed to press home the advantage though and an uninspiring passage of play followed, with both teams unsuccessfully probing solid back lines.
However, as the game appeared to be petering out towards half time, Rangers doubled their lead when Kevin Gallen latched on to Paul Furlong's flick on and calmly slotted home past the keeper.
Much to their credit Brighton responded immediately when, from a corner, Danny Cullip's powerfully struck header beat Chris Day in first half stoppage time.
Rangers responded after the break and Furlong had an early opportunity from an in-swinging free-kick, but his weak header was comfortably saved.
The Seagulls then had a chance to restore parity, but when Oatway's throughball found Knight advancing in on goal, the hotshot lingered and eventually shot wide.
The visitors continued to press for the elusive opening but a well-drilled Rangers defence coped with everything thrown at them.
Rowlands almost scored his second for the home side, forcing a smart save from Roberts after a jinking run, but it was Brighton who looked most likely to score as the final whistle beckoned.
Cullip ballooned a great opportunity skywards before Knight spurned the game's clearest chance forcing a breathtaking point-blank save in the final seconds.