The Bournemouth loanee opened the scoring 12 minutes in, finishing off a fast counter attack and doubled his tally three minutes into the second half with a glancing header.
The Reds were not without chances as Cole Kpekawa and Adam Hammill went close in a stop-start first half, with Adam Davies’ reflex save denying Murray in the opening moments.
Hammill fired just over the top from an angle, Adam Armstrong glanced a header just wide while Josh Scowen drew a fine save from David Stockdale at the end of a flowing move.
Conor Hourihane’s last minute effort had the beating of the goalkeeper, but not the crossbar, landing on the roof of the net as the visitors left empty handed.
Glenn Murray drew the first save from Adam Davies in the opening two minutes, but the Reds ‘keeper stood up well to prevent the striker scoring.
Cole Kpekawa’s reply was to fire a rasping 30-yard effort inches past David Stockdale’s upright with the Brighton goalkeeper struggling to get across to the shot.
The speed of Adam Armstrong caught out Lewis Dunk with only nine minutes on the clock, the Seagulls defender took out the Newcastle loanee as he charged down the wing.
The hosts drew first blood on 12 minutes as a quick counter attack saw Anthony Knockaert race down the right-hand side, before squaring to Beram Kayal, who slotted in Murray to score.
Barnsley did have to play a spell of the match with only 10-men on the field after a nasty-looking head injury to Marc Roberts a quarter of an hour in.
Gaetan Bong received a caution for dissent and Murray came close to a second for the hosts, prodding just wide of the target from six yards out.
Adam Hammill sent an effort spinning just wide of the top corner after good work down the left-hand side and drew a foul out of Bruno just before the half hour, which saw the Spaniard cautioned.
A smart free kick routine from the Reds saw Hammill cross for Sam Winnall, but the forward was flagged offside as his effort drifted wide centimetres wide of the post.
Knockaert’s cross three minutes before the break was almost headed into his own net by Conor Hourihane but Davies was alert to push the ball behind for a corner.
Brighton doubled their lead less than three minutes into the second half as Murray rose highest to glance home Jiri Skalak’s in-swinging free kick, despite the best efforts of Davies to keep it out.
Murray almost completed his hat-trick five minutes after scoring his second, again Skalak was the provider but Murray’s volley was gathered at the second attempt by Davies.
An excellent break, led by Josh Scowen, gave Hammill the chance to drill another effort at goal, this time the ball fizzed over the top of the crossbar.
Scowen received a caution six minutes past the hour mark for a trip on Knockaert and Shane Duffy headed the resultant free kick wide for the Seagulls.
Kpekawa was booked for a strong challenge on Knockaert before a snapshot from Scowen at the end of some fluid passing forced a smart reflex save out of Stockdale.
Sam Morsy and Tom Bradshaw were sent on for the final 10 minutes for Paul Heckingbottom’s side but they could not help the Reds unlock the door.
Hourihane’s dipping effort in the final minute had the beating of Stockdale, but agonizingly landed on the roof of the Brighton stopper’s net, much to the dismay of the 712 travelling fans.
Brighton: Stockdale, Bruno, Dunk, Duffy, Bong, Knockaert, Kayal (Norwood, 46’ ), Stephens, Skalak (Sidwell, 84’ ), Hemed (Baldock, 75’ ), Murray.
Subs: Maenpaa, Murphy, Goldson, Hunt.
Reds: Davies, Yiadom, Roberts, MacDonald, Kpekawa, Hammill, Scowen (Morsy, 80’ ), Hourihane, Watkins (Kent, 64’ ), Winnall (Bradshaw, 80’ ), Armstrong.
Subs: Townsend, Bree, Lee, Jackson.