Welbeck repaid the faith shown in him by Sir Alex Ferguson since the start of the season, with the 20-year-old influential in both United's first two goals, whilst Rooney grabbed his second of the campaign to cap off a fine evening for the Premier League champions.
Sir Alex Ferguson was forced to name a new look backline following injuries to Rio Ferdinand and Nemanja Vidic in last week's clash at West Brom, with Phil Jones and Jonny Evans slotting in at centre-back, whilst Patrice Evra returned to the team at left-back in an otherwise unchanged starting line-up.
The home side got off to lively start, with Younes Kaboul called into action to prevent Danny Welbeck latching on to Ashley Young's low cross, whilst Rafael van der Vaart’s casual loss of possession in the middle of his own half led to an early chance for Wayne Rooney, only for the striker to tamely header Nani's cross into the arms of Friedel.
Indeed the American was forced into action first in the battle of keepers, diving agilely to save Tom Cleverley's well struck effort from the edge of the box that had seemed destined for the bottom right hand corner of his goal.
Not until just before the half hour mark did United threaten again, with Rooney's dinked cross finding Ashley Young in the box, who peeled off Benoit Assou-Ekotto well, only to see his looped header just evade the top right hand corner of the Tottenham goal.
The visitor’s were limited to shots from distance, with David de Gea overcoming the barrage of mid-week criticism and dealing comfortably with efforts from Gareth Bale and Van der Vaart, as the Spaniard instead shifted the focus onto his impressive distribution.
Referee Lee Probert did well to calm a potential flash point between Nani and Kaboul after the winger caught the Frenchman with an outstretched leg, before bringing to a close a half which was void of any real moments of note.
Vedran Corluka replaced Kyle Walker at half time reportedly due to illness, although the 21-year-old had been consistently exposed at right-back throughout the first 45 minutes.
Harry Redknapp's side enjoyed a dominant spell of possession early in the second half, but again lacked the vision and incisiveness to make it count in the final third, with United instead once again peppering the Spur’s goalmouth with shots from Young, Anderson and Rooney in succession.
The deadlock was finally broken after 60 minutes, when Tom Cleverley's fierce cross was met in the air by Welbeck, who drifted in between the Tottenham centre-backs unmarked and guided the ball into the left hand corner of Friedel's goal.
Rooney then went close to doubling the host's lead five minutes later from a free-kick on the edge of the box, before Welbeck audaciously attempted an over head kick as the ball bounced loosely in the area, only for Friedel to be on hand twice to thwart both attempts at goal.
Phil Jones was then on hand to stifle Bale as the Welshman looked to pull the trigger in the opposition box, before De Gea's quick distribution found Young as United were straight back onto the counter-attack.
The ball eventually found its way to Anderson, who fed the ball through to Welbeck in the box, who in turn played a delightful back heeled pass into the path of Anderson that wrong-footed both Michael Dawson and Friedel, with the Brazilian sweeping the ball into the back of the net to give the home side a two-goal advantage.
Spurs were then unlucky not to take advantage of a questionable moment from De Gea, who failed to collect Corluka’s cross whilst under pressure from substitute Roman Pavyluchenko, with Defoe lashing his effort off the left hand post after the ball landed at his feet.
Rooney was on hand to add a third after 87 minutes, rising well to meet Ryan Gigg's cross and nod the ball into the back of the net to cap a convincing display from the current Premier League champions.
The victory puts Ferguson's side level on points with Wolves and rivals Manchester City, with all three sides enjoying a perfect start to the season.