Any doubts about manager Sir Alex Ferguson's decision to field a starting line-up with an average age of just 23 were dispelled just after an hour when 20-year-old striker Welbeck headed in a pinpoint cross from 22-year-old midfielder Tom Cleverley.
Welbeck's superb backheel set up Anderson's sweet strike in the 76th minute and Wayne Rooney added the third with a late header as the champions continued the fantastic home form that propelled them to the title last season.
"The second half we just took off," Ferguson told Sky Sports. "It tells you we still believe in young players... more so when you see the ability they've got.
"The second half performance was absolutely fantastic, I thought it was a really fast game in the first half - end to end."
United, who dropped only two points at Old Trafford on the way to a record 19th league title, maintained their perfect start after last week's win at West Bromwich Albion. Manchester City lead them on goal difference at the top of the fledgling table.
Ferguson kept faith with the youngsters who served notice in the Community Shield season curtain-raiser that they would be keeping the more established players on their toes.
They did not let him down as they game set off at a fast tempo with Cleverley sending Spurs keeper Brad Friedel, almost twice the age of some United players, diving at full stretch to keep out his eighth-minute strike.
Winger Ashley Young headed just wide after a great pass from Rooney as United tested a well-organised Spurs defence.
Tottenham had their own chances but lacked the spark of Luka Modric who had been left out of the team with manager Harry Redknapp saying the Croat's head was "not in the right place" amid speculation he could be leaving the club.
The deadlock was broken in the 61st minute when defender Chris Smalling, another of the new generation at the age of 21, laid the ball back for Cleverley who whipped in a cross that Welbeck sent powering into the bottom left corner.
Bursting with confidence, Welbeck then attempted an overhead kick that landed in the hands of Friedel, while indefatigable Rooney - something of an old hand at 25 - went close with a free-kick that Friedel did well to tip round the post.
Welbeck, back at United after a loan spell at Sunderland last season, set up the second goal with a cheeky backheel to an unmarked Anderson, who sent the ball flying into the net after a move that started at the other end of the pitch.
The third goal owed everything to United's old timers with substitute Ryan Giggs unleashing a right-footed cross that Rooney headed goalwards off the top of his new hair transplant three minutes from time.
"We received a few wise words at half-time and came out from there and fired on all cylinders," man-of-the-match Welbeck said. "Every single point is vital so we need to get as many wins as possible and keep the ball rolling."
Young United keeper David de Gea will have been reli
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