The victory is Chelsea's first on the road in the league since August and means Hiddink remains unbeaten after three games in charge.
It was one year to the day that Alan Pardew was appointed Palace manager and the clubs' respective reversal in fortunes since then remains remarkable given this time last year Chelsea sat top and the Eagles were in the relegation zone.
The teams' overall trajectories remain but Chelsea will take great confidence from a win that moves them up to 14th and demonstrated that European football may still not be out of reach.
Wilfried Zaha, making his 200th appearance for Palace, fizzed an early shot wide but chances were few and far between in the opening stages as torrential rain made keeping possession difficult.
Chelsea playmaker Eden Hazard only lasted a quarter of an hour as he hobbled off to be replaced by Pedro and it was Palace who settled faster, with one Jason Puncheon cross skidding to Fraizer Campbell at the back post but the striker sliced over.
A few weeks ago Chelsea, flustered by their opponents' pace in behind, might have caved but Hiddink appears to have revived some of his side's grit and resilience and instead they took the lead in the 28th minute.
Suitably it was the three players arguably who struggled most under Jose Mourinho involved, as Cesc Fabregas slid a superb through ball into Costa, who pulled the ball back for Oscar to tap home his second goal in four games.
The advantage injected confidence into the visitors, who finished the stronger before half-time as Cesar Azpilicueta chested Oscar's lofted pass into the penalty area but saw his half-volley saved by Eagles goalkeeper Wayne Hennessey.
Chelsea's ascendancy continued after the interval and Kurt Zouma should have scored when he rose above Mile Jedinak at the back post, but the defender headed over the crossbar.
Palace looked vulnerable but their best chance of an equaliser came just before the hour as Campbell played Zaha into the penalty area but the forward scuffed his finish harmlessly into the hands of Chelsea goalkeeper Thibaut Courtois.
It proved a decisive moment as one minute later a loose ball spilled out to Willian and the winger rifled it into the top corner from 25 yards to double Chelsea's advantage.
Having come close to being drawn level, the Blues were suddenly in control and six minutes later they put the game to bed as Willian's shot was weakly parried by Hennessey, allowing Costa to poke in his third goal in two games.
Palace were shell-shocked and it could have been worse at the end as Oscar saw a goal-bound shot blocked, but that was no matter for the travelling supporters who were left singing 'everything is going to be all right' when the final whistle blew.
Wayne Hennessey: 5
Joel Ward: 6
Scott Dann: 6
Damien Delaney: 5
Pape Souare: 6
James McArthur: 6
Mile Jedinak (capt): 5
Lee Chung-yong: 6
Jason Puncheon: 5
Wilfried Zaha: 5
Fraizer Campbell: 5
Marouane Chamakh (for Campbell, 68): 5
Joe Ledley (for Jedinak, 68): 6
Jonny Williams (for Lee, 80): 6
Thibaut Courtois: 7
Branislav Ivanovic: 7
Kurt Zouma: 8
John Terry (capt): 7
Cesar Azpilicueta: 7
Cesc Fabregas: 8
John Obi Mikel: 7
Eden Hazard: 5
Diego Costa: 7
Pedro (for Hazard, 16): 7
Nemanja Matic (for Oscar, 86): 6
The Brazil midfielder remained one of Chelsea's few shining lights amid the gloom that shrouded Jose Mourinho's descent towards the sack. The 27-year-old cajoled Chelsea's attacking game at Selhurst Park, and then provided a thunderbolt strike for the second goal.
MOMENT OF THE MATCH
Wilfried Zaha summed up Palace's toothless attack by spurning a gilt-edged one-on-one with Chelsea leading 1-0 approaching the hour mark. Mere moments later Willian had blasted the ball home for Chelsea's second goal, killing off the tie and twisting the knife even deeper on Zaha's glaring miss.
VIEW FROM THE BENCH
'Lucky' Guus Hiddink lived up to his nickname here, Chelsea's interim manager able to profit as acquisitions from the Jose Mourinho era finally returned to something approaching form.
Cesc Fabregas showed he might just be ready to deliver consistently on the field again and provided the killer pass for an opening goal then laid on by Diego Costa, another alleged villain of this Stamford Bridge season.
Hiddink has persisted with the same 4-2-3-1 formation favoured by Mourinho, but has benefited from the likes of Fabregas and Costa showing signs of recovery since his return for a second stint as interim boss with the Blues.
Palace, meanwhile, continue to suffer the natural shortcomings of a side without a natural goal poacher.
Lee Chung-yong battled manfully slotting in for Yohan Cabaye, but how Palace missed the suspended France midfielder - a nd how Alan Pardew's side struggled without Yannick Bolasie, a long-term absentee with hip trouble.
MOAN OF THE MATCH
Whatever the green shoots of recovery for Chelsea, Eden Hazard remains one Stamford Bridge figure desperately seeking the form of last season.
While the likes of Fabregas and Costa might just be getting their acts together, Hazard continued to look out of sorts before limping off on the quarter-hour mark.
Last year the 24-year-old blasted 19 goals en route to the PFA player of the year award: this term he is yet to register on the score sheet. Chelsea cannot afford to carry a make-weight attacking midfielder, especially given their preference for a lone striker.
TWEET OF THE MATCH
"Excellent day all round. England 629-6 declared while @ChelseaFC call it a day at 3-0. #CFC" - Chelsea fan and former England cricket captain Alec Stewart (@StewieCricket)
Southampton v CRYSTAL PALACE, FA Cup, Saturday January 9
CHELSEA v Scunthorpe, FA Cup, Sunday January 10
Terry told Sky Sports 1: "It was the Chelsea of last year, the football was first-class and we kept the ball in tough conditions.
"The overall performance, as well as the goals, was different class. New year, new start.
"We have to keep winning games. We've had a couple of draws of late and been unlucky not to win more points, we're delighted with three today."
Regarding his new manager, Terry added: "Guus has been great since he's come in. It's unfortunate what's happened, we feel we've let everyone down, but the new man's come in like he did last time and picked everyone up.
"We are where we are, but we're slowly climbing the league table. We've known as a group we had to get better, we've done that slowly but surely."
Palace boss Pardew said: " Chelsea were good today, very good.
"The first 25 minutes was our best period, we had belief about us, but we're lacking a bit of quality at the top of the pitch at the moment and that was evident.
"When you've got a very, very good team and they take the lead, their confidence gets up. Fabregas ran the show in the second half, we couldn't get near him."
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