The in-form Hornets have now taken 13 points from six matches following the arrival of Pearson to significantly boost their survival chances.
It was a result which lifted Pearson’s side out of the relegation zone for the first time this season ahead of Aston Villa’s clash with Manchester City later on Sunday.
Goal-shy Bournemouth contributed to their own downfall on Sunday afternoon and are going in the opposite direction to their opponents after being condemned to a ninth defeat from 11 league games during an alarming slump.
Eddie Howe’s relegation-threatened side began a Premier League fixture inside the drop zone for the first time since December 2017.
But the pair could only watch on in despair as calamitous defending gifted the visitors a 42nd-minute lead.
Stand-in Bournemouth goalkeeper Mark Travers hurriedly gave away possession after receiving the ball back from captain Simon Francis following a poorly-executed short goal-kick, allowing Ismaila Sarr to cross from the right and set up Doucoure for an emphatic close-range finish.
Travers’ costly mistake came after he had been thrust into action for only the third Premier League appearance of his career due to a minor injury suffered by the previously ever-present Aaron Ramsdale.
The Republic of Ireland international had earlier been alert to keep out a low strike from Gerard Deulofeu during a tight opening period short on chances, while Hornets keeper Ben Foster pushed away a Harry Wilson free-kick at the other end.
Since being promoted from the Championship together in 2015, seven of the nine top-flight meetings between the two clubs have ended level.
There appeared little chance of an another draw being added to that statistic when the away side’s lead was doubled with 25 minutes to go.
Record signing Sarr worked space on the right wing and, after his cut back was partially cleared, captain Deeney was on hand to smash his fourth goal in five games into the left corner.
Pearson is Watford’s third manager of a largely forgettable season but his immediate impact has breathed life into the club’s supporters.
The travelling fans chanted his name for much of the second half as Bournemouth rarely threatened an equaliser.
Cherries academy graduate Sam Surridge, who was recently recalled from a loan spell at Swansea, was thrown on for the final 15 minutes but he and misfiring forwards Callum Wilson and Dominic Solanke were unable to break down organised opponents.
Bournemouth have now failed to score in four of their last five league games and their gloom was compounded by a third goal in stoppage time.
Cherries winger Ryan Fraser did well to clear Andre Gray’s initial effort off the line but Argentinian Pereyra was on hand to calmly chest down the ball and hook home, before boos greeted the final whistle.