Victory lifts Palace to within a point of Watford in the Championship table and stretches the club's unbeaten run to six games, although four of those have been draws.
Moses opened the scoring in the second minute after the Hornets had been caught napping by Speroni's long clearance and Lee soon made it two when he rose to nod home Danny Butterfield's cross.
Graham was then denied from the spot and Malky Mackay's side fell further behind in the 54th minute as the in-form Ambrose fired past Scott Loach from the edge of the area to record his sixth goal in as many games.
Warnock made just one change to the Palace side that drew 1-1 with Coventry last weekend, with Moses replacing Freddie Sears, who dropped to the bench.
Jon Harley was recalled to the Watford side in place of Don Cowie, who was missing with a calf injury sustained in training earlier in the week.
The recalled Moses tested visiting goalkeeper Loach in the opening minute.
And a minute later, the youngster put Palace ahead as he latched onto a long clearance from Speroni and beat two defenders before firing a low shot into the bottom-right corner.
Palace extended their lead in the sixth minute as Lee headed home a hanging right-wing cross from Butterfield.
Shaun Derry then fired wide from distance and Neil Danns volleyed over the bar from 12 yards as Palace continued to dominate the opening period.
Watford finally managed a shot of their own shortly after the half hour, but Henri Lansbury's 25-yarder sailed past Speroni's left-hand post.
The Palace stopper was called into action soon after to save a close-range header from Graham, while at the other end Loach kept out a similar effort from Lee.
The Hornets were handed a golden opportunity to level on the stroke of half-time when Lee brought down Lansbury in the penalty area, but Speroni produced an outstanding save to keep out Graham's spot-kick.
Palace then wrapped up the points nine minutes after the interval as Darren Ambrose twisted and turned before beating Loach from 18 yards.
With the visitors on the rack, Loach reacted well to tip away a strike from the lively Moses.
Soon after, Watford's Craig Cathcart was denied by Speroni after he had headed goalwards from Tom Cleverley's corner.
But the Eagles remained in control and substitute Calvin Andrew twice came close to adding a fourth in the closing stages.
A miserable day for the Hornets was completed in injury-time as Cleverley's shot struck the post.