Harry Kane responded to a host of missed chances by heading the late goal that secured Tottenham’s 1-0 victory at Crystal Palace.

The England striker spurned three earlier opportunities but retained his composure to secure all three points and strengthen Spurs’ pursuit of a top-four finish.

Kane’s late intervention came as a blow to Roy Hodgson, the manager who handed him his international debut but who is now fighting to keep Palace in the Premier League.

Amid injuries to 12 senior players, Palace’s Hodgson handed a debut 20-year-old defender Aaron Wan-Bissaka, who started at right-back, and gave new striker Alexander Sorloth his first appearance at Selhurst Park.

Even if the likes of absentees Wilfried Zaha, Mamadou Sakho, Yohan Cabaye and Ruben Loftus-Cheek had been fit, a draw would have represented an encouraging result for Palace so their discipline and organisation proved little surprise.

Content to concede possession to their visitors and deploy Christian Benteke as their sole attacker, they limited Spurs’ space and options and refused to be stretched by one of the division’s most potent and expansive teams.

The visitors’ only true sight on goal during the first half fell, predictably, to Kane, but even then only after an error from Patrick van Aanholt. When the left-back clumsily directed Dele Alli’s ball into the striker’s path, Kane was gifted a fine chance from directly in front of goal but the impressive Wayne Hennessey did well to spread himself and palm his shot wide.

Palace’s only response came through a header Sorloth tamely nodded straight to Hugo Lloris, which was followed, early in the second half, by Kane again missing from similar range.

This time Christian Eriksen, after Serge Aurier’s flick-on, sent possession into Kane’s path, but having connected well and had both time and space, he wastefully struck wide of the right post.

Aurier saw another close-range effort, after being fed by Alli, saved by Hennessey when shooting too close to the goalkeeper, who then did well to deny Ben Davies.

When the hosts struggled to clear a corner from Eriksen, the loose ball fell to Davies, who connected well when shooting on the turn before seeing the diving Hennessey save in the bottom left corner.

Alli, whose reputation was defended by Hodgson this week after recent suggestions of diving, had a penalty appeal dismissed when he went down under minimal contact with the goalkeeper, before the third of Kane’s misses.

The 24-year-old was this time played into the area by substitute Lucas Moura, and similarly to an earlier finish he dragged just wide of the left post.

It was in the 88th minute, from Eriksen’s corner, that he finally scored. Meeting the Dane’s delivery at the back post, he headed goalwards and saw his effort find the back of the net after Hennessey could only get a hand to it.

If it was cruel on Palace and their goalkeeper, it was also Kane’s 35th goal of the season, and 150th of his club career. Defeat leaves Palace in 17th place, where only goal difference keeps them out of the bottom three.