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.
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 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."
