The Seagulls were within 10 minutes of a first victory over their arch rivals on home soil since 1988, and a return to the top of the table, following Craig Mackail-Smith's early opener.
But Wilfried Zaha struck a deserved equaliser and substitute Ambrose put the visitors ahead before Murray rammed the taunts of the Seagulls faithful back down their throats with the third.
It meant a first league defeat for Brighton at their new Amex Stadium, which was packed to the rafters for a spiky derby encounter.
The Albion fans had reserved a special 'welcome' for Murray, who fired them to promotion last season only to snub a new contract and instead join Palace on a free transfer.
Brighton boss Gus Poyet promptly went out and signed Mackail-Smith, the only player to outscore Murray in League One, and the £2.5million striker showed why after just seven minutes.
Ryan Harley played a short corner to Gary Dicker, who was allowed to reach the byline and cross towards the near post where Mackail-Smith prodded the ball home.
These two sides, from opposite ends of the A23, had not played each other in six years but absence did not appear to have made the heart grow fonder.
Referee Andy D'Urso was kept on his toes in a first half not for the faint hearted, booking Zaha and Peter Ramage of Palace and Brighton's Liam Bridcutt and Lewis Dunk for some particularly meaty challenges.
Murray had a chance to silence the boo boys when he was sent through by Jonathan Williams shortly before half-time but, with Dunk in close attendance, he scuffed his shot wide.
But Palace were far more of a threat after the break and Zaha got the better of Marcos Painter on the hour mark but his angled shot was deflected over.
From the corner Brighton survived a major scare when goalkeeper Casper Ankergren missed Sean Scannell's cross, Paddy McCarthy headed goalwards and Mackail-Smith proved he could be handy at both ends by clearing off the line.
Ankergren redeemed himself by beating away Jonathan Parr's fierce drive and Murray was inches wide from a Zaha cross.
But Palace's pressure eventually told in the 80th minute when Zaha skipped past two weak challenges on the edge of the area before cutting his shot back past Ankergren.
Ambrose stabbed them into the lead with a minute to go from Parr's cross, and Murray added insult to injury when he curled in number three in stoppage time.
Brighton Ankergren, Taricco (Vincelot 59), Greer, Dunk, Painter, Bridcutt, Dicker, Harley (Vicente 69), Barnes, Mackail-Smith, Noone (LuaLua 64).
Subs Not Used: Brezovan, Hoskins.
Booked: Bridcutt, Dunk.
Goals: Mackail-Smith 7.
Crystal Palace Speroni, Ramage (Parr 51), McCarthy, Tunchev, Moxey, Wright (Ambrose 78), Jedinak, Williams (Gardner 90), Zaha, Scannell, Murray.
Subs Not Used: Price, Easter.
Booked: Ramage, Zaha, Moxey.
Goals: Zaha 80, Ambrose 89, Murray 90.
Att: 20, 968
Ref: Andy D'Urso (Essex).