Key players Asmir Begovic and Younes Kaboul were sold against Grant's wishes in January.
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The visitors were now rampant and Kaboul doubled their lead after skipping round Stephen Pearson and driving home.
However, former Spurs team-mate Younes Kaboul has indicated he will turn down a move to the Stadium of Light.
The visitors were always in command after Eduardo's free-kick had deflected in off Younes Kaboul to give them an early lead.
Elsewhere, the Swiss-based Afghan group Ensemble Kaboul and Mahwash, described as Afghanistan's best traditional band, were winners in the Asia-Pacific category.
Keane has also had an offer accepted for centre-back Kaboul, who endured a frustrating first season at Spurs after arriving from Auxerre.
Polish striker Jelen broke the deadlock after 31 minutes when a simple long ball out of defence from Kaboul evaded Hemdani and Karl Svensson.
"The transfer of Younes Kaboul was completed and Portsmouth pressed for an immediate payment in order to alleviate their cashflow situation, " said the Tottenham statement.
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Papa Bouba Diop dropped down to the bench, along with Younes Kaboul, but if any concerns that the big midfielder would be missed were soon dispelled.
Spurs were creating chances, too, Pavlyuchenko heading Kaboul's cross wide at the near post and Bale excellently denied one-on-one by Jaaskelainen after Jermain Defoe's clever through-ball.
Portsmouth, to their credit, created the odd half chance in reply, a Younes Kaboul tackle denying Brown inside the box and Kanu scuffing wide when well placed.
These included Stoke completing a deal for keeper Begovic on a four-and-a-half-year contract, striker David Nugent's loan deal being extended at Burnley, while Tottenham re-signed central defender Younes Kaboul.
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Saha, on his 200th Premier League appearance, controlled the ball and struck it low beyond the advancing James after a pass from the half-way line eluded centre-back Younes Kaboul.
Any deal for the forward, who has scored six goals in 32 appearances for England, also took into account monies owed to Tottenham by Portsmouth for Younes Kaboul and Pedro Mendes.
Though solid at the back, with right-back Younes Kaboul particularly impressive, Spurs' efforts to press forward more often than not broke down thanks to a poor touch or good Bolton defending.
The versatile Finnish international became Sunderland manager Roy Keane's first summer signing on Wednesday, but is set to be joined at the north-east club by Pascal Chimbonda, Steed Malbranque and Younes Kaboul.
Taylor had a left-footer from range saved on the stretch by Gomes in the home goal, while only a Kaboul block stopped the same player's goalbound effort levelling the scores with Gomes stranded.
The home side created chances of their own though to kill the game and thought they had done so when Begovic dropped the ball under pressure from Younes Kaboul and Pavlyuchenko hooked in.
Kaboul, 22, has also attracted interest from Aston Villa and Portsmouth and his agent has suggested that Pompey would be the youngster's preferred destination, which would leave Keane continuing to look for a centre-back.
The financial problems have also impacted upon the hierarchy at the club, with chief executive Peter Storrie and manager Avram Grant claiming last week that they had been unaware of negotiations concerning the sale of Kaboul and Begovic.
BBC: Portsmouth provide players & staff with wages assurance
As expected, Spurs dominated possession from the outset, although in the opening half-hour their best chances were two Younes Kaboul headers from corners, one smartly pushed aside by Ali Al Habsi, the other cleared off the line by James McCarthy.
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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Redknapp's men then believed they were the victims of injustice when Younes Kaboul turned in Hutton's pass as the referee's assistant ruled the ball had already gone out of play - but they did not have to wait long to take the lead.
West Ham took the lead when Younes Kaboul's headed clearance looped in off the chest of Matthew Upson in the 52nd minute before Danny Webber rescued a point for Pompey in the 76th minute when he slotted the ball through the legs of Hammers goalkeeper Robert Green.
Bottom-of-the-table Portsmouth -- who agreed to sell defender Younes Kaboul to Tottenham this weekend just so the wage bill could be paid -- went behind when Emmanuel Adebayor fired City ahead with his first goal since his traumatic experience with Togo at the Africa Cup of Nations in Angola.
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