The Harry Kane team could be grateful to Christian Eriksen. Tottenham Hotspur – to give them the name that the Manchester City manager, Pep Guardiola, contentiously did not – were desperate for a first Premier League win at Wembley; no title challenge can withstand ropey home form. Thanks to Eriksen, one of their other stellar performers, they got it.

It was a scratchy game and Tottenham were a long way from their best. But Eriksen helped to settle their nerves with what proved to be the winning goal early in the second half, and they can look forward to a big week with optimism. They visit Real Madrid in the Champions League on Tuesday night and host Liverpool next Sunday.

Tottenham’s focus did not waver from the task in hand. After damaging draws here against Burnley and Swansea City, Mauricio Pochettino could not contemplate further dropped points against opponents that his team knew they ought to be beating. Eriksen’s smart finish swung the contest and it did not matter that Kane, unusually, was off-colour.

Tottenham could also be grateful to Hugo Lloris. The goalkeeper made a stunning reflex save in the first half to keep out a ricochet off Eric Dier, while he denied the substitute, and former Spurs favourite, Jermain Defoe, on 78 minutes.

Eddie Howe had surely been aware of Tottenham’s difficulties in breaking down deep-sitting opponents at Wembley, and so he started with five at the back and flooded the midfield. It was a practical gameplan, rather than one shaped by his more expansive instincts, and he felt that his players executed it well.

Bournemouth battled, they kept their shape and they had a couple of flickers in the first half. Adam Smith cut back for Junior Stanislas, but his effort squirted off Davinson Sánchez and flew wide, with Lloris grounded, and, from the corner, the ball came off Dier. Lloris needed to get down low to block.

Pochettino had lost Ben Davies to illness and he reported that the defender would probably not be fit for Madrid. In Davies’s absence, the manager switched to a 4-2-3-1 formation, with Jan Vertonghen at left-back. His team were sluggish in the first half, their movement ahead of the ball poor, the cohesion absent. Apart from one effort by Kane, which Asmir Begovic saved, they offered little.

Pochettino had to do something and he did. He changed to 3-4-2-1 for the second half, with Dier making the third centre-half but stepping up when Tottenham did not have the ball, and Eriksen moving into central midfield.

He would unlock the stalemate almost immediately.

There was a fortuitous element to the goal and, from a Bournemouth perspective, it was certainly a bad one to concede. Simon Francis jumped into a tackle on Eriksen, after Son Heung-min’s pass, and it was one that he had to make. But the ball wriggled underneath him and ran perfectly for Eriksen. He opened up his body, wafted his left foot and guided the ball low into the far corner.

Tottenham moved the ball with greater pace in the second half and the game became more watchable. Kane had a header ruled out for offside before he was twice denied by Begovic. It was not Kane’s day and, as if to emphasise the point, he shinned a volley so far wide on 65 minutes that the ball went out for a throw-in.

Howe went for broke, introducing Defoe and switching to 4-4-2. How close Defoe would be to the equaliser. Fastening onto a pass from another substitute, Jordan Ibe, he struck low for the near post, but Lloris saved with his legs.

Tottenham finished strongly, with Eriksen working Begovic, Dier seeing a shot blocked by Steve Cook, Dele Alli heading wide and two substitutes, Moussa Sissoko and Georges-Kévin Nkoudou, failing to finish off a stoppage-time break – Begovic cleaned out Nkoudou on the edge of the area and Harry Winks lifted the follow-up high. Nkoudou was forced off and Tottenham would play out time with 10 men.

“I’m so happy to win at Wembley in the league because I can now avoid these questions for the rest of the season,” Pochettino said, with a smile. “It wasn’t a great performance but we deserved it.”