Former Manchester United, Everton and England star Rooney had the hosts 2-0 ahead by half-time at Audi Field, with his second goal, a delicate lift over opposition goalkeeper Nick Rimando, the pick of his trio of strikes, completed with a tap-in in the 65th minute.
Rooney then turned provider, his delivery picking out Lucas Rodriguez to smash home a stunning fourth from just outside the area before Ulises Segura capped off the rout with 10 minutes to go.
Real Salt Lake's case was fatally undermined by the dismissal of Jefferson Savarino for a dangerously high boot in first-half stoppage time, and he was joined in making an early exit by Marcelo Silva for committing a second bookable offence in the 67th minute.
Columbus Crew is level on seven points with DC United courtesy of a 1-0 win at home to Dallas, with Montreal Impact one point back following a 3-1 victory at Orlando City.
Alex Muyl netted a brace as New York Red Bulls came from a goal down to brush aside San Jose Earthquakes 4-1 at home.
In the Western Conference, Seattle led through first-half goals from Victor Rodriguez and Jordan Morris, Nicolas Lodeiro's penalty making it 3-0 in the 49th minute.
Raheem Edwards got one back for Chicago seven minutes later, and Fabian Herbers scrambled home a second to raise the prospect of a nervy finish to the contest for Seattle.
But Raul Ruidiaz got in behind the Chicago defence in the 88th minute to score in his eighth consecutive MLS match and restore Sounders' two-goal cushion.
The 4-2 victory was a third win from the first three matches of the season for Seattle for the first time since 2009, leaving them two points clear of Houston Dynamo, who had Memo Rodriguez's brace and a penalty from Alberth Elis to thank for their 3-2 win at home to Vancouver Whitecaps.
In the final match of the day, LA Galaxy saw off Minnesota United 3-2 at home to join their opponents on six points from three matches played.