Nketiah’s thumping effort into the roof of the net increased Arsenal’s lead against bottom-of-the-table United.
A sensational strike from 25 yards completed a perfect afternoon for the England forward Nketiah, who has five league goals this season, all of which have come at home.
Fabio Vieira scored a late penalty after the video assistant referee (VAR) adjudged Oliver Norwood to have fouled him inside the area.
Takehiro Tomiyasu got on the end of a flick from Mohamed Elneny and poked home from a corner in stoppage time.
Victory lifted Arsenal up to second in the table, two points behind north London rivals Tottenham.
The Gunners are unbeaten in 19 home games against United in all competitions since 1971.
Once they got in front, it seemed there would only be one outcome.
United keeper Wes Foderingham saved fierce efforts from Gabriel Martinelli and Ben White as Arsenal asserted their dominance.
Nketiah came into the starting line-up in place of Gabriel Jesus, who injured a hamstring in the midweek Champions League win against Sevilla, and took his opportunity with both hands.
He was alert to Rice’s pass, taking a brilliant touch to wrongfoot Auston Trusty and fire home.
Foderingham flapped at a corner from Bukayo Saka and Nketiah pounced to slam in a half-volley from close range.
The confidence on display from Nketiah seemed to increase with each finish, culminating in a superb third.
A lay-off from Emile Smith Rowe, making his first start of the season, gave Nketiah time and space to blast into the top corner. With less than an hour played, the match ball had been secured.
“It’s amazing. It’s not been easy – last month I lost my auntie so I want to dedicate these three goals to her. Her family was here watching so it is a really special moment,” Nketiah told BBC Match of the Day.
Nketiah let Vieira take the penalty, sacrificing the chance to become only the third Arsenal player to score four goals in a Premier League match after Andrey Arshavin and Thierry Henry.
“My first instinct was to grab the ball and go, but Fabio won it and it was a good moment. It’s all about being a team player. It was his time to get a chance and he tucked it away,” added Nketiah
Saka was captain in Martin Odegaard’s absence and, when he was substituted, he passed the armband to Nketiah, who captained Arsenal for the first time.
Jesus could only applaud in the stands as he watched Nketiah put in an accomplished display.