The former Stoke City boss was confirmed before the match as the man to fill the void left by Ian Holloway at the end of October, and he saw Barry Bannan's strike end an eight-match winless run in the Premier League despite Yannick Bolasie's dismissal.
Bolasie, who had been one of Palace's better players, saw red with 13 minutes to go for a foul on Jake Livermore, but the visitors showed remarkable resilience to wrap up three vital points to move of the foot of the table.
Palace survived a late scare when Livermore hit the woodwork before the visitors scrambled it clear, earning them just their second league win of the campaign.
Hull manager Steve Bruce opted to make three changes from the side that lost 4-1 to Southampton last time round, with Allan McGregor returning following a lengthy thigh injury, while Robert Koren replaced Liam Rosenior.
There was just one change for the visitors, with caretaker boss Keith Millen opting to bolster their attack by including Dwight Gayle at the expense of Jerome Thomas.
It was the hosts who started the brighter and Yannick Sagbo squandered a fine chance to put them ahead after just two minutes, steering a low shot just wide of the post from close range.
Bolasie was Palace's most positive attacking outlet but he struggled to make a meaningful impact without the help of his team-mates and became increasingly isolated as the half wore on.
The game remained primarily a midfield battle before the break, though Robbie Brady did nod wide for the hosts, while George Boyd finally tested Julian Speroni with a powerful effort in the 42nd minute.
There was action at either end early in the second half, Sagbo firing straight at Speroni before Gayle was thwarted at the end of a swift counter-attack.
The visitors had another fine chance in the 65th minute, and it fell to Bolasie, but after weaving through a number of players his hurried shot went well wide of the mark.
Bolasie's next involvement saw his day come to a premature end after he lunged in on Livermore, but Bannan stunned the home crowd with a low effort from inside the box with just nine minutes left.
Hull threw men forward late on and almost levelled when Livermore hit the post but the visitors held on.
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