Four of the goals came in the first half at St. James' Park, through Jacob Murphy, Harvey Barnes, Fabian Schar as well as an unfortunate own-goal by Marc Guehi.
Sandwiched between them was a penalty for Palace by Eberechi Eze that was saved by Newcastle goalkeeper Nick Pope.
Alexander Isak added a fifth goal in the 58th minute - his 21st of the campaign - as Newcastle followed up their 4-1 hammering of Manchester United on Sunday to make it six wins in a row in all competitions.
That streak included a victory over Liverpool in the English League Cup final for a first major trophy in 70 years.
Newcastle jumped above Nottingham Forest to move within four points of second-place Arsenal, and look in good shape for a return to the Champions League next season.
The Premier League will have five representatives and Newcastle are five points clear of sixth-place Chelsea with six games remaining.
The dominant display will have made for good viewing for Newcastle manager Eddie Howe, who is recovering in the hospital after being diagnosed with pneumonia.
Howe also missed the Manchester United match but Newcastle are doing just fine without him at the moment.
Palace conceded five goals for the second straight game, having lost 5-2 at Manchester City on Saturday.
15°C