The Dutchman struck for the first time in a month as he netted United's third in a one-sided Barclays Premier League encounter at Old Trafford.
Van Persie's form had been the subject of heavy scrutiny ahead of the game after an ineffectual display in the previous week's win at Arsenal.
It was thought the 31-year-old could even lose his place with Radamel Falcao fit again after injury.
But manager Louis van Gaal kept faith with his compatriot and was rewarded as Van Persie wrong-footed James Chester on the edge of the area and rifled a left-footed shot into the roof of the net after 66 minutes.
"If you score a goal like that it gives you confidence and the team, and if I am really honest I needed that," said Van Persie, who also teed up United's second goal for Wayne Rooney.
"You just have to keep working and those goals, or any goals, will come."
United have now won three in succession in the league for the first time under Van Gaal, who described the performance as the most satisfying of his time in charge.
The only obvious downside was the loss of record signing Angel di Maria early on with a hamstring injury
The Argentinian will be assessed but Van Gaal has already ruled him out of Tuesday's clash with Stoke.
Hull were never in Saturday's contest, with the tone set as Rooney shot narrowly wide after five minutes.
Chris Smalling bundled in their deserved opener after a goalmouth scramble in the 16th minute
Goalkeeper Allan McGregor twice had chances to defuse the situation but ultimately could only help the ball over the line, as confirmed by the goal decision system.
Rooney struck from the edge of the area three minutes before half-time and United's dominance could have yielded several more goals.
Substitute Falcao had one of their best chances and looked certain to make it 4-0 in the dying moments but Michael Dawson blocked on the line from point-blank range.
Defender Smalling agreed with Van Gaal's assessment of the game.
The 25-year-old said: "The manager said it was our best game of the season and I think it was
It was a complete performance.
"I think he said of the Arsenal result that we ground that out without particularly playing well, but this time we did.
"He's said he wants six points (this week) and we want to deliver that on Tuesday against Stoke."
Smalling played alongside Marcos Rojo in a flat back four, with wingers Antonio Valencia and Ashley Young in the full-back positions.
Van Gaal has previously shown preference for a three-man defence but felt he had the flexibility to adapt because players are growing used to his philosophy.
The United manager said: "It is not (about) methods, it is philosophy
We have to perform because of that philosophy and then you can play in different formations, and that we are doing.
"It is also dependent on the quality of the opponent
We selected the right formation I think to beat a team with five defenders."
Hull had just 23 per cent of possession during the game and were ruthlessly punished for their defensive mistakes.
After beginning the season with confidence following last season's comfortable survival and FA Cup final appearance, the Tigers' form is now a cause for concern.
Steve Bruce's men are without a win in six matches and have lost their last four
They only stayed outside the bottom three on goal difference on Saturday night.
Former Tottenham defender Dawson told Tigers TV : "It is always a worry because you are down there
You have to win football matches to get out of it
"People are talking about having the best squad here for many years, but it is only the best squad if we make it the best squad.
"The points table at the end of the season will define that.
"But we can't get too down
We have to pick ourselves up because the games come thick and fast in December
We have got to stick together
Losing here is not going to define our season."
Source : PA
Source: PA