Spurs easily sealed qualification from Group A with a game to spare, a remarkable achievement for a side whose last campaign among Europe's elite came almost half a century earlier.
In fact, it is arguable whether any team have made such a thrilling impact on their Champions League debut as Harry Redknapp's great entertainers, who have now added the scalp of an admittedly depleted Bremen to those of holders Inter Milan and Dutch champions FC Twente.
They may be very much wild-cards when it comes to the knockout stage but no-one will want to come to White Hart Lane and face the likes of Gareth Bale, who picked up where he left off against Inter three weeks earlier.
North London derby match-winner Younes Kaboul opened the scoring in the sixth minute, Luka Modric made it 2-0 and Bale missed a penalty before Peter Crouch wrapped up the points, while there was a welcome clean sheet after 17 matches without one.
Tottenham could have been forgiven for starting cautiously in the absence of injured talisman Rafael van der Vaart but they were on their way after barely five minutes, a succession of corners eventually seeing the ball worked to Aaron Lennon.
The winger beat Dominik Schmidt all too easily before crossing for the unmarked Kaboul to fire home first time.
Schmidt, one of two debutants in an injury-ravaged Bremen team, tried to make amends when he glanced Aaron Hunt's corner over the crossbar.
They visitors enjoyed a boost when Jermaine Jenas limped out of the action to be replaced by Wilson Palacios in the 20th minute.
But they should have been 2-0 down two minutes later, Bale crossing for the recalled Crouch, whose knockdown was sliced horribly high and wide by Roman Pavlyuchenko.
Spurs provided a hint as to why they had not kept a clean sheet for three months when Lennon presented the ball to the dangerous Marko Marin, who scuffed wide from 20 yards.
Lennon quickly returned to the day job, though, skinning Sebastian Prodl and crossing for Pavlyuchenko, who should have finished first time but took a touch that allowed Per Mertesacker to block.
Clemens Fritz's frustration at his Bale torment boiled over when the Bremen right-back was booked for hauling the latter back.
Kaboul nodded over Bale's corner before Spurs doubled their lead in stoppage-time, Alan Hutton crossing and Crouch causing enough mayhem to allow Modric to nip in with a brilliant piece of control and ice-cool finish.
Having scored four, four and three in their three previous Champions League home games, it appeared a matter of how many Spurs would rack up in the second half.
Their first chance came when Prodl was cautioned for felling the flying Lennon and Bale sent a 51st-minute free-kick against the bar.
The winger then produced a sensational cross for Crouch, whose point-blank header somehow hit Prodl and ricocheted behind.
Moments later, Tottenham were awarded a penalty when debutant Felix Kroos tripped Modric just inside the box.
However Tim Wiese guessed the right way to save Bale's weak 53rd-minute spot-kick and Prodl was on hand to clear the rebound. Bremen immediately withdrew Kroos - who had been booked - for Onur Ayek, while Spurs soon followed with Jermain Defoe for Pavyluchenko.
Defoe quickly showed his two-month injury lay-off had cost him none of his pace, the England striker racing onto Modric's ball and firing a fierce shot Wiese did well to parry.
If new captain William Gallas had any doubt his north London derby performance had won over his doubters among the Spurs fans, it was dispelled when he was treated to an affectionate chant after thwarting a Marin attack.
Tottenham showed no sign of sitting back, with several crosses going begging and Bale drilling inches wide after being found by Defoe.
They finally got the third goal their dominance deserved 11 minutes from time when Bale's cross hit the bar and Lennon cut back the rebound for Crouch to steer home.
Bale was soon withdrawn for Niko Kranjcar to a deserved standing ovation and a rest ahead of bigger tests to come.