Newcastle managed only two shots on target. Vicente Guaita was at full stretch to keep out a long-range effort from Joelinton and tipped over a fierce effort from Fabian Schar.
And to round off a thoroughly disappointing day for the visitors, January signing Valentino Lazaro was shown a straight red in stoppage time for hauling down Wilfried Zaha, who was through on goal.
The win moves Palace above Newcastle into 13th with 33 points. Newcastle drop down to 14th, with 31 points, seven clear of the drop zone.
The Eagles managed six shots on target in a one-sided first half - equalling their best in an entire game this season - with Dubravka thwarting them twice with two remarkable saves.
Both Ayew and Zaha were allowed plenty of space against a Newcastle side set up with five at the back. Ayew in particular impressed, coming in from the right to produce seven efforts on goal - five of which were on target.
This was a better attacking display from Palace, but they played a Newcastle side in a generous mood.
Joelinton only managed two touches in Palace's box in the entire match, something we see only too often.
That is now no goals in three matches for Steve Bruce's side, and the discussions over striker Joelinton's inclusion in the XI will become more heated.
The Brazilian, signed for £40m in the summer, has scored only one goal in the league and this week his boss suggested the Brazilian was not a natural goalscorer but a "team player".
There is little argument over the 23-year-old's workrate but, like Bruce also said, he needs to be more selfish.
The forward did bring the travelling support to their feet with his brilliant first-half strike which was kept out by Guaita, but it is in the penalty area where the fans want him to impose himself.