Luka Modric's attempted pass to Robbie Keane came to him off Sebastien Bassong and he found the net at the second attempt.
The visitors were rewarded for a strong start when Emile Heskey robbed Sebastien Bassong and squared for Marc Albrighton to slide in and convert.
Spurs made an unconvincing start on the plastic pitch and were 3-0 down inside 28 minutes before Sebastien Bassong and Roman Pavlyuchenko reduced the deficit.
Robin van Persie opened the scoring from the penalty spot, his league-leading 27th goal this season, after on-loan Tottenham defender Sebastien Bassong was sent off for pulling the Dutchman down.
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Michael Owen was out of contract at the end of last season and joined Manchester United, while Sebastien Bassong, Obefami Martins, Damien Duff and Habib Beye have all departed recently.
Campbell wriggled clear of the attentions of Sebastien Bassong and Assou-Ekotto and burst into the box, before going over an appalling forward's challenge from Luka Modric, who simply hung out a leg.
Harry Redknapp's team remained on top and Modric's shot deflected off Bassong on the line for Harper to save before Bent headed over from Alan Hutton's pinpoint cross to the far post.
Twente striker Bryan Ruiz robbed Sebastien Bassong of possession and, after racing clean though on goal, tried to chip a shot over keeper Heurelho Gomes, who stuck out a vital hand to excellently save.
Portsmouth wanted a penalty from the resulting corner as they claimed Butt had handled in the area and moments later Defoe looked despairingly at the referee as he went down under a challenge from Sebastien Bassong, but again nothing was given.
Bentley did at least sting James's palms with a long-ranger, while Sebastien Bassong should have done better with an unmarked header from a corner that he directed straight at keeper James and Crouch slid a golden chance wide in stoppage time.
Gallas, who will also provide competition to centre-backs Michael Dawson, Sebastien Bassong and Younes Kaboul, was not registered for European competition so he will be unable to play against Young Boys in the second leg of Spurs' Champions League qualifier on Wednesday.
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Then after a spell of crisp passing, Heskey created the opener when he outmuscled Bassong, got to the byeline and rolled the ball across goal for Albrighton to slide in ahead of Hutton and apply the finishing touch for his first senior goal.
Shearer expressed concern that Newcastle would struggle on the pitch in the Championship unless the team's off-field problems were swiftly rectified, allowing a new manager to strengthen a squad whose departures have included Michael Owen, Obafemi Martins, Mark Viduka, Habib Beye and Sebastien Bassong.
Liverpool, who were without the injured Steven Gerrard and Fernando Torres, showed their defensive discipline to keep out Spurs and should have been out of sight by the time they were awarded an injury-time penalty after David Ngog was brought down by Sebastien Bassong.
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