Ashley Young also scored a brace as the Red Devils ran riot at Old Trafford.
Danny Welbeck gave United the lead in the 22nd minute, looping a header over Wojciech Szczesny in the Arsenal goal, before having to go off with a hamstring injury.
Young made the visitors pay six minutes later, curling an effort into the far corner from outside the area.
It was three before half-time when Rooney bent a free-kick over the wall and into the top corner.
Arsenal pulled a goal back in first-half injury-time when Walcott fired through de Gea's legs.
After the interval, Rooney sent Szcezny the wrong way with his second free-kick of the match, before setting up the fifth.
His pass went through Laurent Koscielny's legs to Nani, who chipped the ball over the keeper.
Substiute Park Ji-Sung made it six before van Persie scored Arsenal's second.
Arsenal have now had a player sent off in each Premier League game this season after Carl Jenkinson received a second yellow for a challenge on substitute Javier Hernandez.
Rooney completed his hat-trick from the spot after Walcott was adjudged to have brought down Evra.
It was eight when Young scored a similar effort to his first in stoppage-time.
United lead the table after three games, while Arsenal sit just above the relegation zone, in 17th.