The Eagles midfielder headed the home side in front in 38 minutes and then 10 minutes into the second half doubled Palace's lead with a 25 yard free-kick for his seventh goal from his last seven matches.
The first half was stop-start affair with Kit Symons heading against the post, before Black finished off a slick move on the right which resulted in Julian Gray delivering the perfect cross to the far post.
Palace had already wasted two free-kicks taken from the edge of the box but Black showed how it should be done with a low right foot effort which went through the Preston wall and nestled neatly into the left corner.
Dele Adebola missed two absolute sitters before being substituted for Ade Akinbiyi, who made his first home appearance of the season after a long lay off.
Preston will be disappointed as they managed just one shot on target which came from Paul McKenna just before the break.
Although the visitors had fair share of possession in the second half Palace comfortably sat on their lead and Kolinko in the Palace goal was rarely troubled.
Palace boss Trevor Francis said: "We were good value for our win and Preston can't complain about the outcome. We were outstanding in the first half but we lost the plot in the second half.
"We are proving a difficult side to beat once we go in front and it's down to appetite for hard work.
"I've got players here that work harder than they thought they could possibly work. We are functioning much better as a team."
Craig Brown said: "Palace deserved to win and I have no complaints. It was a good performance from Tommy Black but we should have done better."