The encounter started positively for the Cherries, though, as they took the lead with what was the fastest Premier League goal of the season so far.
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There was 49 seconds on the clock when the ball was worked to Matt Ritchie and the Scotland international made the most of the space that he was afforded by firing his shot beyond visiting goalkeeper Hugo Lloris.
However, the North Londoners - unbeaten since being defeated by Manchester United on the opening day - were behind for just eight minutes thanks to Harry Kane, who scored his second goal of the campaign from the penalty spot after he had been hauled down inside the area by home keeper Artur Boruc.
In response to the equaliser Ritchie created an opening for Josh King, but the Norwegian frontman was unable to keep his header on target and that miss was then duly punished with 17 minutes played when Spurs took the lead.
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The visiting North Londoners now had complete control of the proceedings and they went on to score their third goal in the 29th minute, with Boruc at fault. The Pole was unable to hold Kane's deflected cross and when the ball broke free, Erik Lamela was on hand to tap in from close range.
As the half drew to a close the hosts almost reduced the arrears to just one on goal on two occasions, but first Marc Pugh's effort was hacked off the line by Spurs defender Toby Alderweireld and then King's low strike cannoned off the post.