Jay Rodriguez made it a happy homecoming as his tenth goal of the season edged the Clarets ever nearer the play-off places.
Rodriguez's third-minute goal was just enough to earn Burnley their tenth home victory of the campaign, exactly a month after their last game at Turf Moor.
The spectacular strike was a worthy winner but despite some outstanding football in the first half it took a first clean sheet since Eddie Howe's first game in charge to lift the Clarets up to seventh place in the table.
Bring Me Sunshine ...
The lack of a second goal made it a nervy finish but having toughed it out, Burnley made it just one defeat in their last nine games as they climbed above Leicester City to keep the top six firmly in their sights.
Not surprisingly Howe had stuck with the same side that won at Preston a week earlier and the Clarets picked up where they left off with a later winner at Deepdale by going ahead with virtually their first attack.
Rodriguez can do little wrong at the moment and the young striker continued his rich vein of form when he cracked a stunning 25-yarder into the top corner to move into double figures for the season.
Two years on from scoring the first League goal of his career against the same opposition, the England under-21 international again showed how far he has come as he gained a measure of revenge for his frustrating afternoon at Selhurst Park in September when he did everything but score in a goalless draw.
Rodriguez's early strike was the cue for a dominant first-half performance in which the Clarets were virtually camped in Palace's half.
The relegation strugglers briefly promised to respond with Michael Duff having to block well from dangerman Darren Ambrose.
But thereafter it was almost a game off attack against defence up to the break.
The one frustration for the Clarets was their inability to force the second goal and put the game to bed against a side with only one away win all season.
Rodriguez went close to a second when he headed wide a cross from Tyrone Mears, whose combination with a re-vitalised Ross Wallace was a constant source of potential for the home side.
The on-song frontman then cracked an effort over the top after Jack Cork had stepped over a corner from Wallace.
And when Wallace again prised open the Palace defence seven minutes before half-time, Cork arrived late to meet his cross with a header which was just too close to goalkeeper Lewis Price.
With the Clarets not able to drive home their superiority it was in danger of becoming a frustrating afternoon as Palace, aware they were still in the contest, began to grow in confidence early in the second half and Ambrose went close with a free-kick which dipped onto the roof of the net.
Howe reacted by sending on Wade Elliott in a bid to regain the Clarets' earlier forward momentum but again it was Ambrose who threatened with a set-piece as he thundered in a free-kick which Grant turned spectacularly over the bar.
Grant saves from Ambrose
And the Clarets lived dangerously again with 14 minutes to go when another free-kick caused uncertainty in the penalty area.
When the ball dropped invitingly six yards out Palace captain Paddy McCarthy should have scored but instead he skied his effort over the top as the Clarets held on to secure a vital three points.
Burnley: Grant, Mears, Fox, Carlisle, Duff, Marney, Cork, Eagles (Alexander 87), Iwelumo (Elliott 60), Rodriguez, Wallace (Edgar 90). Substitutes: Bartley, Bikey, Easton, Jensen.
Crystal Palace: Price, Clyne, Moxey, McCarthy, Gardner, Wright (Easter 81), Ambrose, Danns, Dikgacoi (Scannell 69), Iversen (Counago 69), Vaughan. Substitutes: Davis, Barrett, Zaha, Speroni.
Booked: Danns 27, Iversen 45
Referee: Andy D'Urso.