The Hornets had gone into the contest seeking a fourth straight success, but they were completely outplayed in the first half as the visitors spurned numerous opportunities to gain the upper hand.
But the goal they deserved arrived in the 57th minute when Dicko converted a low Rajiv van La Parra centre.
The Hornets did hit the woodwork twice in the last 15 minutes but, in truth, an equaliser would have been harsh on their opponents.
Wolves had come into the game with only one win in their last eight league games, but they were left wondering how they did not take the lead during an excellent opening 20 minutes in which they caused their hosts numerous problems.
Along from the quality of their finishing, the main reason the visitors did not make the breakthrough was down to the excellence of Heurelho Gomes, who made two high-class saves to keep his side level.
The Brazilian first showed fine reactions to get down and divert a close-range effort from Dave Edwards behind after being set up by Kevin McDonald, before surpassing that with a spectacular full-length save to tip over an excellent 30-yard strike from Bakary Sako.
Watford did manage to weather that storm but shortly after the half-hour mark a fine Sakho through ball cut apart the Hornets’ defence and put Dicko through on goal, but he passed up a golden opportunity by sliding the ball wide of the target.
The home side needed to change something at the start of the second period because they had been so disappointing for much of the opening 45 minutes and head coach Slavisa Jokanovic opted for a change in formation from 3-5-2 to 4-4-2.
Initially it looked like the move might pay dividends as the home side began to at last offer an attacking threat, with Matej Vydra and Daniel Tozser forcing Carl Ikeme into his first saves of the match.
But any hopes the Hornets had of building on this were ended in the 57th minute when Wolves got the goal their first-half display had so deserved.
Van La Parra was the instigator as he attacked the left side of the defence and got to the byline before laying the ball across for Dicko to convert the simplest of chances to make it 1-0.
Jokanovic made three changes as he tried to galvanise his troops to get back in the game and they did go close from a couple of goalmouth scrambled before, in the 74th minute, substitute Odion Ighalo took advantage of a defender slipping to fire in a shot which almost surprised Ikeme as he pushed it on to his crossbar at the near post.
That looked like being the home side’s best chance of an equaliser until the game entered stoppage time when Ighalo was again denied by the woodwork after being found in the area, this time with Ikeme beaten.