The on-loan Brighton winger claimed his fourth goal of the season as the Cottagers overcame the absence of 18-goal leading scorer Aleksandar Mitrovic to move within four points of second-placed Leeds.
Mitrovic was ruled out with an ankle injury picked up in Saturday's win at Hull and is expected to be out for up to three weeks.
Boro – who arrived as Craven Cottage as the division's in-form side following their recent upturn in results – a third game in six days proved too much as they suffered a first defeat in six league outings.
The Cottagers quickly showed they were capable of overcoming the loss of their main forward during a blistering opening.
Knockaert immediately demonstrated his threat by cutting in from the right before firing over with a left-footed shot.
Instead Boro were forced to focus on keeping a foothold in the game after Knockaert had given the home side a sixth-minute lead.
It was the perfect start for Parker's side who should then have gone on to put the game out of Boro's reach in the opening half hour.
Fulham's approach play was exhilarating as Knockaert set up Josh Onomah for a shot that was well saved by Aynsley Pears before Ivan Cavaleiro shot over after being sent clear on goal by Bobby Decordova-Reid.
Onomah and Cairney squandered further openings yet while Parker was entitled to be pleased with his side's display, the Fulham boss will have been concerned at their failure to make the pressure tell.
And that feeling was only reinforced when Boro left-back Hayden Coulson's cross was deflected against the bar in the 31st minute before Marcus Tavernier somehow directed a close-range volley over from the resulting corner.
Boro continued to improve after the break, enjoying more possession, but striker Rudy Gestede wasted a good headed opportunity to level.
And it was Fulham who regained control in the latter stages although they were unable to find the finish that would have made for a more comfortable end to the game.