Premier League: Man United 3 Hull 0
The Dutchman came in for some flack after last weekend's 2-1 win at former club Arsenal, with manager Louis van Gaal claiming the striker had a "very bad game".
However, playing a key role in two goals at Old Trafford on Saturday will help restore confidence in his abilities, as United registered three wins in a row for the first time this season.
Chris Smalling opened the scoring in scrappy fashion in the 16th minute, after Angel di Maria had given the hosts cause for concern when he left the field clutching his right hamstring.
Van Persie teed up Wayne Rooney to smash in a second from 20 yards three minutes before half-time, and the 31- year-old rounded off the win with a delightful left-footed strike.
The result lifts Manchester United to fourth in the Premier League, while Hull have now gone six matches without a win and sit above the bottom three on goal difference alone.
Of the three central defenders who started last weekend's 2-1 win over Arsenal, only Smalling retained his place in the United back line, with Marcos Rojo lining up alongside him and Michael Carrick playing just in front, while Hull brought James Chester and Mohamed Diame in for Tom Huddlestone and the suspended Gaston Ramirez.
It was United captain Rooney who got the first sight of goal – opening up his body to curl wide of the right-hand post from 20 yards in the seventh minute.
Van Gaal's decision to keep Smalling in his defence paid dividends in the 16th minute, when the 25-year-old broke the deadlock amid some questionable Hull defending.
The visitors failed to clear a corner, and the ball eventually found its way just over the line when Smalling drove goalwards after Allan McGregor had attempted to scoop away.
Smalling claimed the goal, but McGregor appeared to knock the ball over his own line.
The ineffective Hatem Ben Arfa was hauled off 10 minutes before the break in favour of Sone Aluko, but Hull were soon two down.
Juan Mata chipped the ball forward for Di Maria's replacement, Ander Herrera, who in turn nodded the ball down for Van Persie on the edge of the penalty area. The Netherlands forward played the ball back for the advancing Rooney to drive home from 20 yards and give United a comfortable cushion at the interval.
Van Persie almost opened his own account with a header that was well palmed over by McGregor, although the linesman's flag had already gone up for offside, but the ex-Arsenal man got his goal 24 minutes from time.
After picking the ball up on the edge of the penalty area, Van Persie created the angle for himself to rifle in a powerful left-footed effort.
Hull were largely impotent in attack throughout - a Jelavic header after 76 minutes about as close as they came - and United were comfortable in seeing out a deserved victory, which could have been even more convincing had Michael Dawson not been on hand to block Radamel Falcao in the six-yard box in stoppage time.