Moura created goals for Harry Kane and Son Heung-min and bagged one himself as Tottenham comfortably beat a Palace side for whom manager Patrick Vieira missed the game because of a positive COVID-19 test.
While victory moved Tottenham up to fifth in the table, it proved a dispiriting day for Palace who were reduced to 10 men in the 37th minute when Wilfried Zaha was sent off.
By that time Tottenham were well in control after Kane swept in from Moura's pass before Moura headed the second.
Son wrapped up the Boxing Day win with his side's third from close range in the 74th minute.
Tottenham have 29 points, six less than fourth-placed Arsenal but have played three games fewer after having two matches postponed this month because of Covid-19.