Tottenham, competing in the Champions League for the first time, will now avoid the likes of Barcelona, Real Madrid and Bayern Munich in the draw on Friday 17 December.
It is quite a turnaround for a team who, less than four months ago, found themselves 3-0 down after 28 minutes against Young Boys in a play-off just to reach this competition.
They are still without an away win in Europe's elite club tournament since 1961, but that might not be a major concern to boss Harry Redknapp given his side's prolific form at White Hart Lane.
Redknapp vowed to go all out for the win and despite making four changes to his starting line-up it was still a strong Tottenham team that took to the field.
And although the temperatures dropped below freezing before kick-off, the visitors warmed the hearts of their supporters by opening the scoring - albeit in bizarre fashion.
Twente actually made the more promising start and Wout Brama saw a half-volley from 20-yards saved by a diving Heurelho Gomes before the Brazilian goalkeeper reacted well to stop a Luuk de Jong flick from Rosales' dangerous cross.
But the hosts looked on in disbelief as Boschker went to clear captain Peter Wisgerhof's bobbling back-pass, only to swing at thin air and watch the ball trickle into his net.
It was a horrid way for the 40-year-old, in his 21st season at the club, to mark his Champions League debut.
Yet the goal came against the run of play and, fortunately for Boschker, Twente were soon level after a stinging volley from Rosales struck the raised elbow of Benoit Assou-Ekotto.
Landzaat's initial spot kick was disallowed - the former Wigan midfielder punished for stopping during his run-up - but an unconvincing second effort squirmed home via the legs of Gomes.
There was further bad news for Spurs when Jermaine Jenas was forced off with what appeared to be a recurrence of his recent calf injury. The midfielder was cautioned for the length of time he took to leave the field and will be suspended for Tottenham's next European match.
After an early howler, Boschker made a fine late stop to earn Twente a point
While clear-cut chances were few and far between before half-time, Roman Pavlyuchenko had a drive well saved and Defoe's near-post volley sailed narrowly wide as Spurs worked hard to regain their advantage.
And shortly after the restart they had it, Twente failing to clear Gareth Bale's left-wing cross and substitute Aaron Lennon brilliantly teeing up Defoe to slot past Boschker.
That goal made Spurs the first team in Champions League history to score two or more in all six of their group games.
But back came Twente and the Dutch champions, bidding for their first home Champions League win and a maiden triumph against English opposition, levelled through Rosales' precise header from Theo Janssen's centre.
Yet the highly rated Janssen swiftly morphed from hero to villain, losing possession in midfield and allowing Wilson Palacios to surge into the box. After the Honduran's shot was parried, Defoe was on hand to poke in.
Tottenham may have been expected to sit back and protect their lead but they continued to surge forward and this encouraged Twente to hit them on the counter-attack.
Michen Preud'homme's men went close on several occasions before Lennon was penalised for a challenge on Marc Janko and Chadli got the better of Gomes with a sublime curling set-piece.
Both sides pressed hard for a winner and Gomes drew a fine one-handed save from Brama before Boschker made a smart block to prevent Douglas turning Bale's cross into his own net.
But the spoils were shared after a pulsating 90 minutes and few could argue with that outcome.
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