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Gareth Bale went close to breaking the deadlock with a ninth-minute header, but it was the home side who had made the better start.
Lewis Holtby was given his debut for Spurs as a 70th-minute substitute and showed signs of early promise.
Andre Villas-Boas's men were back on level terms with 10 minutes remaining when Bale finished following a breakaway, and suddenly they were in the ascendancy.
However, Bale and Defoe were both frustrated in their attempts to snatch all three points as the Canaries held on for a draw.