Chelsea also won their match 1-0 to move to third (temporarily).
United provisionally moved 15 points clear at the top after the convincing win.
Japanese midfielder, Kagawa, opened the scoring just before halftime and grabbed two more well-taken goals in the second half.
Rooney added the icing on the cake with a long-distance screamer in injury time as United warmed up for its Champions League match against Real Madrid in style.
In other venues, Chelsea provisionally moved into third place thanks to Demba Ba’s 28th-minute winner, giving Coach Rafa Benitez some respite after his midweek tirade against the club’s fans.
Also at the St Mary’s Stadium, struggling QPR stunned their host, Southampton, as they piped the Saints 2-1 away from home.
The win will give Sir Harry Redknapp and his team some glimpse of hope that they can still survive the drop.
Also, Victor Anichebe’s Everton secured a 3-1 win over Reading; while West Ham got a valuable away win over Stoke City as the Hammers ran home with a lone goal victory.
Sunderland and Fulham settled for a 2-2 draw in their own fixture
In sunday’s star fixture, Arsenal and Totenttham Hostpurs, will slug it out in the London derby as the race for top four finish enters a crucial bend.