But central defender Clarke Carlisle salvaged a point in the dying minutes when he came up to head home Jermaine Wright's cross.
Dyer was a thorn in Leeds' side all night with his pace. His first was a well-taken strike from Heidar Helguson's accurate cross, the second after Leeds had clawed their way back into the match, came from a dreadful mistake by Sean Gregan.
The Leeds midfielder over-hit his pass to Paul Butler putting Dyer clear on goal and he made no mistake from eight yards out.
Dyer's ninth minute effort was the second match running Leeds had gone behind to an early sucker-punch and even though they hit back, they never looked likely to repeat the 6-1 hammering they inflicted on QPR four days earlier.
Needing to beat Watford by two goals to climb above them into 11th place, Leeds started brightly but there were early signs that the pace of Dyer and James Chambers would cause them problems.
Dyer's first goal meant that after a run of eight clean sheets in ten games, Leeds have failed to stop the opposition scoring in the last nine and they came close to going further behind but Neil Sullivan leapt to claw away a goal-bound header from Dyer.
And the home defence was let off once more after Dyer dragged Danny Pugh into the centre, leaving Chambers unmarked but he only managed to drag his shot wide of the far post.
It was midway through the half before Leeds regained any momentum and the goal when it came was worth waiting for.
Butler's long ball into the box was laid into the path of Wright by Brian Deane and the former Ipswich midfielder drove his shot low and hard into the corner of Richard Lee's net for his third goal in five matches.
Leeds dominated most of the rest of the half but the best chance still fell to Watford, Jack Smith making a good run down the right and driving the ball across the six-yard box only for Brynjar Gunnarson to slide in and put his shot over the bar.
The most exciting incidents of the match were crammed into a couple of minutes, Sullivan again producing a brilliant save to deny Sean Dyche, the ball then breaking straight down the other end where Lee palmed away a header from David Healy under pressure from the athletic Sean Dyche.
But in the end it was a scrappy mistake that provided the breakthrough and a straightforward header that saved the point.