Puncheon rocketed home another crucial goal for Palace in the 16th minute after collecting his own rebound following an excellent break down the right wing by Yannick Bolasie.
His latest strike hauled Palace level on points with Hull, who were just a point outside the top 10 when the teams kicked off.
Back-to-back wins have put clear water between Palace and the drop zone, which looked unthinkable when they were floundering at the bottom just two months ago.
Hull paraded their January purchases, giving a first run-out to their new strikeforce of Shane Long and Nikica Jelavic.
But the £14million duo barely got a sniff as the Tigers slipped to a fourth straight defeat, a run which has seen them gradually sucked back into the relegation battle, and they ended the match with 10 men as goalkeeper Allan McGregor saw red in added time.
Palace enjoyed the better start on a wet London night, with two chances to take the lead in the opening three minutes.
First a well-worked free-kick sent Dean Moxey round the back of Hull’s defence and his shot was deflected just wide.
And from the corner Mile Jedinak was inches away from prodding into an empty net but the Eagles skipper could not adjust his feet in time as the ball fizzed past.
In the 16th minute Palace did take the lead, but only after a big moment of controversy went in their favour.
Long was certain he should have had a spot-kick when he tumbled in the area as the outpaced Danny Gabbidon scrambled to get back.
The striker definitely had a point as he was first to a high ball over the top and was then sent sprawling amid a tangle of legs – but referee Roger East was having none of it, to the disbelief of Hull manager Steve Bruce.
And Bruce’s mood worsened moments later as Palace charged down the other end and promptly took the lead.
There was more than an element of fortune about the goal as well.
Bolasie reached the byline and his cross, at the second attempt, reached Puncheon whose initial header was flying well wide.
However, it hit the back of team-mate Marouane Chamakh and fell perfectly for Puncheon to crash high into the net.
Jedinak almost added another with a fierce free-kick which McGregor tipped over the crossbar.
The closest Hull came to an equaliser in the first half was in stoppage time when Julian Speroni was almost embarrassed by a free-kick from Tom Huddlestone, which was swerving wildly before the Palace keeper managed to swat it clear.
Hull did improve after the break but Palace stood firm as Jake Livermore blazed over and Long hit the side-netting.
Jelavic’s evening was summed up when he sliced horribly into the stand behind the goal and Liam Rosenior passed up Hull’s best chance when he prodded Livermore’s low cross wide from a couple of yards out.
Hull’s misery was compounded when McGregor was shown a second yellow card in stoppage time following his clash with Stuart O’Keefe.
With Bruce having used all his substitutes, Huddlestone ended the game in goal as Hull desperately sought an equaliser.