Palace were awarded a penalty following a VAR check for handball by Hassane Kamara and Zaha stepped up to slot home his 13th goal of the season after sending Watford goalkeeper Ben Foster the wrong way.
The visitors needed a win and a mathematical swing to keep alive their dwindling hopes of surviving the drop but their timid display meant Palace comfortably kept Watford at arm's length.
Watford's task of scoring at least two goals became even more difficult when they were reduced to 10 men in the second half after Kamara, booked for handball earlier, was shown another yellow card for a foul on Michael Olise.
Foster kept Watford in the contest with a string of fine saves, ensuring Palace's dominance did not reflect on the scoreline, but his teammates offered little in attack and fell to their sixth straight league defeat.
Patrick Vieira's side climbed up to ninth place on 44 points while Watford remained second-bottom with 22 points.