Barnes tucked away his ninth goal of the season to cancel out Chris Martin's opener, which also came from the spot after controversial referee Stuart Attwell took centre stage.
Both decisions appeared soft, Will Buckley penalised for fouling Wilfried Zaha and then Buckley tumbling under Nathaniel Clyne's challenge.
But Brighton were not complaining as they avoided a double defeat to their old foes after they were beaten at the Amex Stadium back in September.
Palace fans were just pleased to see Zaha and Clyne in the line-up, laying to rest rumours of their pre-deadline departures to the Premier League.
The Eagles turned down Bolton's improved bid for Zaha and the winger soon began to show why he is so highly rated.
He tormented Adam El-Abd with one jinking run and cross which Buckley had to head narrowly wide of his own goal, and shortly before interval his snap-shot was well saved by Peter Brezovan.
But Brighton have their own flying winger in Buckley, the hero of Saturday's FA Cup win over Newcastle, and his charge to the byline and pull back should have been converted by Craig Mackail-Smith but his close-range shot was straight at Julian Speroni.
Barnes could have put the visitors ahead after Mackail-Smith chested a high ball into his path but Palace's Paul McShane, who scored the winner for Brighton on their last visit to Selhurst six years ago, got a brave block in.
In the second half Martin fizzed a 20-yard shot narrowly over Brezovan's crossbar and Sean Scannell scuffed his shot in front of goal from another Zaha cross.
Zaha blotted his copybook when he reacted angrily to a tackle from Barnes, lifting the Brighton striker up and dropping him to the ground to earn a booking.
But predictably the teenager was at the heart of the action when Palace took the lead.
Buckley's challenge in the area looked innocuous but Zaha hit the deck, referee Attwell pointed to the spot and Martin stepped up to bury the spot-kick.
But 10 minutes later Attwell levelled things up when Buckley this time went down easily under a challenge from Clyne and Barnes smacked home the equaliser.
Speroni saved well from Inigo Calderon in stoppage time to preserve a point for the hosts.