Tottenham (8-3-0) enters the match now fourth in the league standings.
A 66th-minute goal by 20-year-old center back Juan Foyth was enough to earn Spurs a ninth win in 12 league games this season.
Mauricio Pochettino insisted he never had any doubt goalkeeper Hugo Lloris would repay his faith after the French number one kept Crystal Palace at bay as Tottenham ground out a 1-0 win at Selhurst Park.
A change of shape midway through the first period helped the visitors take a strangehold of the game, with Dele Alli dropping deeper to influence the game on his first Premier League start in over two months.
Tottenham have been far from their sparkling best so far this season, but it's worth nothing they are fourth in the Premier League and still fighting to qualify out of their hard Champions League group.
Spurs continue their impressive start.
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Starting XI: Hennessey (6); Wan-Bissaka (8*), Tomkins (7), Sakho (7), van Aanholt (6); Kouyate (6), Milivojevic (7), McArthur (7); Townsend (6), Ayew (6), Meyer (5). Subs: Kelly 6, Schlupp 7, Sorloth 4.
With a double to save Tottenham's Champions League campaign against PSV Eindhoven on Tuesday, Kane took his goalscoring tally to 10 goals from 15 matches in all competitions.
Substitutes: Aurier (7), Son (6), Winks (6). They have lost nearly all their big games and have been nowhere near their seductive best, yet they are still in the Champions League, just about, and a win today would take them to within two points of the leaders Manchester City.
Crystal Palace have been floating around the middle of the table for most of the season but after getting only one point in their last five games, Palace are only two points above the bottom three.
As for Palace, they'll be without key man Wilfried Zaha as he failed a late fitness test due to a slight muscle injury.
While Palace had again struggled in the final third, they defended soundly and played with greater belief than they last did when Zaha also missed out in September's 2-0 defeat at home to Southampton.