Those results have ensured that Brighton have been able to climb up to 16th in the Premier League standings. They currently have 26 points from 24 games, and have a point more than Newcastle United at the moment.
However, Brighton are still not completely out of the woods in terms of being dragged into a relegation scrap. They have just four points more than Fulham, who beat bottom club Sheffield United on Saturday.
In their last Premier League game, Brighton drew 0-0 with Aston Villa to extend their unbeaten league run.
Palace, on the other hand, have shown inconsistency recently. Following two excellent wins against Wolves and Newcastle United, they lost their last two league games against Leeds and Burnley.
They were dire in their last game, which they lost 3-0 to the Clarets at Selhurst Park. Johann Berg Gudmundsson, Jay Rodriguez and Matt Lowton scored in that game, as Roy Hodgson's side were put to the sword.
Palace currently have three points more than Brighton this season, and sit in 14th place.
Brighton and Hove Albion vs Crystal Palace Head-to-Head
Brighton have won 40, while losing 37 of the 104 clashes that they have had against Crystal Palace.
In the reverse fixture at Selhurst Park earlier this season, Alexis Mac Allister scored a 90th-minute goal to earn a point for Brighton. Wilfred Zaha had opened the scoring for Crystal Palace.
Brighton and Hove Albion form guide: D-L-D-W-W
Crystal Palace form guide: L-L-W-W-L
Brighton and Hove Albion vs Crystal Palace Team News
Brighton and Hove Albion
Solly March could miss the rest of the season with a knee injury. Tariq Lamptey's thigh injury will continue to keep him out of action as well. Striker Florin Andone and defender Adam Webster are also ruled out for this game.
Injured: Solly March, Tariq Lamptey, Adam Webster, Florin Andone
Zaha is a huge miss for Crystal Palace, with the star attacker suffering from a hamstring problem.
Defenders James Tomkins, Mamadou Sakho and Joel Ward are all injured. Meanwhile, there are doubts over the fitness of midfielders James McArthur and James McCarthy.
Injured: Wilfred Zaha, Mamadou Sakho, James Tomkins, Joel Ward
Doubtful: James McArthur, James McCarthy
Brighton and Hove Albion vs Crystal Palace Predicted XIs
Brighton and Hove Albion Predicted XI (3-4-1-2): Robert Sanchez; Ben White, Lewis Dunk, Dan Burn; Joel Veltman, Yves Bissouma, Pascal Gross, Steven Alzate; Alexis Mac Allister; Neal Maupay, Leandro Trossard
Crystal Palace Predicted XI (4-4-2): Vicente Guaita; Nathaniel Clyne, Scott Dann, Cheikhou Kouyate, Patrick van Aanholt; Jordan Ayew, Luka Milivojevic, Jairo Riedewald, Eberechi Eze; Christian Benteke, Michy Batshuayi
Brighton and Hove Albion vs Crystal Palace Prediction
Brighton are playing some excellent football in recent times. They have been able to marry that with being solid defensively, and not conceding too many goals.
The Seagulls have not conceded more than a single goal in any of their last 10 games. Given Palace's injury concerns and inconsistencies, we are predicting a narrow win for Graham Potter's side.
Prediction: Brighton and Hove Albion 1-0 Crystal Palace