Norway international Parr scored his first goal in a Town shirt to break the deadlock, forcing the ball in from close range after Jay Tabb had been denied then Murphy extended the lead three minutes from time with a terrific volley on the run.
Town stayed with the same team that beat Millwall at the weekend, while Brighton included former Blues’ loanee David Stockdale in goal.
Bruno Saltor cleared from David McGoldrick as the Town striker attacked Paul Anderson’s free-kick in the first opening of a quiet first 15 minutes, Anderson then throwing himself at Tyrone Mings’ cross, his header bouncing wide of the far post.
Anderson threatened again soon after, ghosting in to get on the end of Mings’ cross but his header went wide.
Dean Gerken was down sharply to his left to deny Danny Holla in Brighton’s first effort at goal but it was Blues who went closest to breaking the deadlock in the first half hour, McGoldrick releasing Murphy but the Republic of Ireland striker couldn’t keep his shot under the bar as Stockdale raced out.
McGoldrick whipped in a cross that beat everyone, while at the other end Tabb had to be alert to block Kazenga LuaLua’s effort on the edge of the box.
Gerken did superbly to beat out Sam Baldock’s strike, McGoldrick pulling a 25 yard free-kick wide of Stockdale’s right hand post in the last action of the first-half.
Town were indebted to Gerken again straight after the break, the ‘keeper’s right foot preventing Gordon Greer’s header from a corner finding the net.
Blues had a shout for handball on the edge of the box from Parr’s shot but referee Christopher Sarginson waved away the appeals, McGoldrick going close with a header.
Gerken saved well from LuaLua as the game opened up, Anderson seeing his shot blocked by Joe Bennett as Town searched for the opener.
Anderson had another effort at goal, his volley not testing Stockdale but the Brighton ‘keeper produced a brilliant save a minute later to keep out Mings’ audacious flick from McGoldrick’s cross.
Holla then wasted a good chance for the Seagulls blasting high over the bar after Craig Mackail-Smith had set him up on the edge of the box.
McGoldrick weaved some magic before seeing his cross held by Stockdale before Mick McCarthy made his first change, Alex Henshall on for Anderson for the final 20 minutes, Luke Hyam soon following for Teddy Bishop.
Mings tested Stockdale again with a right foot effort low down after more good work by McGoldrick before Blues made the breakthrough on 78 minutes, Mings crossed, Tabb was denied by Stockdale but Parr forced the ball in from close range.
Stockdale held firm from Tabb’s free-kick, Gerken did the same at the other end from LuaLua before Murphy sealed the points for Blues three minutes from time with a superb finish from Mings’ long pass down the left to take Town into eighth place in the Championship.