Both scored, either side of a Michael Carrick header, to significantly boost their top-four hopes, with the striker's celebration responding to a recent video of him boxing
England and United captain Rooney headed into Sunday's match amid an unusual media furore after footage emerged of him being supposedly floored in a mock boxing bout with Stoke City full-back Phil Bardsley at his home.
Rooney ensured he had the last laugh with a boxing-themed celebration when he put United 3-0 ahead in the 34th minute, completing a first half where nothing went right for the visitors at Old Trafford.
|VIEW FROM OLD TRAFFORD
|By Paul Macdonald
Manchester United have all but ended Tottenham's top-four challenge with a commanding 3-0 win at Old Trafford that should provide some relief after a difficult week for Louis van Gaal.
Tottenham may have been terrible but in the opening 45 minutes the likes of Wayne Rooney, Michael Carrick and Marouane Fellaini gave Spurs little time to settle and were clinical when the chances came their way.
United's problems are far from solved but head to Anfield in seven days time with their confidence returned, in what could be a season-defining clash.
But they were faced with a relentless United side as goals from Marouane Fellaini and Michael Carrick inside the first 20 minutes set Louis van Gaal's men on the way to a victory that leaves them just two points behind misfiring neighbours Manchester City, who are second.
The excellent Carrick was one of three players to come into the United line-up following Monday night's dispiriting FA Cup quarter-final loss to Arsenal, alongside Juan Mata and Phil Jones, while Danny Rose was preferred to Ben Davies at left-back in Tottenham's only change.
There was an initially nervy start from United as David de Gea spared Jones from an embarrassing own goal in the third minute following a rash backpass.
But more sizeable holes in Tottenham's defensive set-up were soon apparent as Carrick strode into midfield unchallenged to play a measured throughball that Fellaini steered across Hugo Lloris and into the bottom corner in the ninth minute.
Roles were reversed 10 minutes later when Fellaini's attempt from Mata's in-swinging corner was partially cleared and Carrick calmly picked his spot with a fine header against his former club.
United were cutting Spurs to ribbons down the left flank, a state of affairs that prompted Pochettino to replace winger Andros Townsend with Mousa Dembele.
The 31st-minute substitution could not prevent the hosts from landing a seemingly inevitable knockout blow on their punch-drunk opponents.
Nabil Bentaleb carelessly coughed up possession on halfway, allowing Rooney to tear through a retreating and dishevelled Tottenham defence before firing home.
Dembele wasted a rare opening for Pochettino's men early in the second half, while Bentaleb made an important block to thwart Daley Blind at the other end.
The earlier ferocious pace had understandably subsided by the time that Ander Herrera lashed into the side netting in search of United's fourth.
Tottenham suffered no further damage, but their first defeat in six outings against United had long since been a formality - in-form striker Harry Kane prevented by De Gea from reducing the arrears in the 89th minute.
Old Trafford rose to welcome a late Premier League debut for highly rated youngster Andreas Pereira, but it was an afternoon when their long-time hero Rooney stole the limelight.