In what was almost a mirror image of their play-off round first leg at Young Boys, Spurs romped into a two-goal lead in Germany and could easily have been three or four up before half-time.
But a suicidal four-minute spell either side of the restart turned their Group A clash on its head and they could have easily returned to London empty-handed.
In the end, a draw was just about what both sides deserved as Spurs learnt another valuable lesson about the harsh realities of Champions League football.
A straightforward win had looked on the cards for the opening 43 minutes as a Petri Pasanen own goal and a superb Peter Crouch header saw the visitors take a stranglehold on proceedings.
But Hugo Almeida halved the deficit completely against the run of play and Marko Marin levelled before both sides missed glorious chances to win it.
Redknapp stuck with the 4-5-1 formation which he experimented with in Saturday's 1-1 draw at West Brom.
He had vowed to be more cautious away from home in Europe following last month's game at Young Boys, who had raced to a 3-0 lead inside half an hour.
Avoiding that kind of start tonight was vital against a side who were anything but Champions League rookies, Bremen returning to Europe's top table after their five-year run in the competition was ended last season.
But it was the Germans who were slow out of the blocks tonight, allowing Tom Huddlestone and surprise starter Jermaine Jenas early long-range efforts.
Bremen were struggling to contain Tottenham's new talisman Gareth Bale and after two early warnings he made them pay in the 12th minute.
Benoit Assou-Ekotto's brilliant ball released him down the left and his low cross was turned in by Pasanen under pressure from Crouch.
Marko Arnautovic glanced a tough header wide as Bremen tried to respond but it got better for the visitors in the 18th minute.
Jenas played a sensational volleyed pass to Rafael van der Vaart on the left and the new man produced a pinpoint cross for Crouch to power a header back across Tim Wiese and into the net.
The home side were living dangerously and the outstanding Bale almost made it 3-0 when he robbed Clemens Fritz and raced clear.
His shot was parried by Wiese and Jenas was narrowly beaten to the rebound.
Bale saw another effort beaten away by Wiese nine minutes before the break as Bremen's injury-hit defence continued to buckle.
Home boss Thomas Schaaf immediately responded by throwing on Hunt for Philipp Bargfrede and it appeared to have the desired effect two minutes from the break when Almeida got between recalled Spurs captain Ledley King and Assou-Ekotto to nod in Wesley's superb inswinging cross.
Almeida then scuffed a shot through a crowd of bodies a minute later as Bremen looked for a hugely undeserved equaliser.
Incredibly, they did draw level two minutes after the restart.
Carlo Cudicini had just tipped Hunt's shot over following a Younes Kaboul mistake when Marin stuck a fierce low drive that skidded off the wet surface and past the goalkeeper at his near post.
Stunned Spurs immediately replaced the injured Van der Vaart with Robbie Keane.
Almeida went close again and Marin nearly weaved his way through a clutch of bodies just before the hour mark.
Tottenham regained some semblance of control in a game that was looking wide open until Jenas was yellow-carded for a cynical trip on Wesley.
Marin was then given the freedom of the Weserstadion to cut in from the left and fire a low shot narrowly wide of the near post before Bremen withdrew Wesley for Tim Borowski for the final quarter of the game.
The rain which had been falling steadily from kick-off suddenly abated but the pressure on the Spurs defence did not.
Hunt missed a glorious chance to complete Bremen's comeback 17 minutes from time when another error gave him a clear sight of goal from 10 yards.
Redknapp shored up his midfield by throwing on Wilson Palacios for Aaron Lennon, with Bremen responding by withdrawing Almeida for Sandro Wagner.
With both sides pressing for a winner, Bale whipped in a devilish low cross that somehow evaded three of his team-mates.
And with just over three minutes remaining, Palacios played in Crouch for a glorious chance to win it but the England striker's clipped finish drifted wide.
There was still time for Hunt to blast a shot straight at Cudicini and for Borowski to be booked for felling Assou-Ekotto before the game ended in what was probably a deserved draw. 