This was one of those games whereby Pep Guardiola’s body language told almost all of the story. Manchester City may have cut Liverpool’s advantage at the top to a point but their inadvertent weapon of choice here was more pair of scissors than sledgehammer. The sight of Guardiola crouching on the edge of his technical area, restlessly peering either side of the assistant referee Darren Cann to analyse the picture as Bournemouth burst to breaking point in search of an equaliser provided a snapshot of quite how uncomfortable a ride this proved.

Guardiola’s nervous energy is for good reason. They are, ostensibly, in a three-way title race and he spent much of his post-match press conference with one eye on a television at the back of the room showing Arsenal’s joust with Newcastle. City have their eyes fixed on winning a sixth Premier League title in seven seasons and their quest to clinch a second Champions League resumes against Copenhagen next month. Then there is the FA Cup, a fifth-round trip to Luton next up on Tuesday.

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“They are supermen,” Guardiola said of his players. “Our fans have to be so proud of these guys. Bournemouth had seven days to prepare, seven days of dreaming of beating the best team in the world. We had three. The calendar is so demanding, the expectations are so high.”

City, beaten once since October, are a formidable force but Bournemouth were anything but cowered by the challenge and picked holes in the champions, with Marcus Tavernier missing two chances to restore parity. Phil Foden scored the only goal midway through the first half and with Erling Haaland uncharacteristically blunt in attack, by the end Guardiola felt the need to introduce Kevin De Bruyne, back from a niggling hamstring injury, with six minutes of normal time to play. Even after that the Bournemouth substitutes Dango Ouattara and Enes Unal went close to replying, the latter heading wide. Bernardo Silva felt compelled to make a crude tactical foul on the advancing Antoine Semenyo with added time looming. Bournemouth have not won in seven matches but should take heart from taking the champions all the way.

Bournemouth have a wretched record against City – they have now lost all 14 top-flight meetings by an aggregate score of 45-7 – but there was never any danger of a repeat of the 6-1 trouncing at the Etihad Stadium in November. Haaland was thwarted in his efforts to get on the scoresheet in the second half, Illia Zabarnyi blocking his shot from an acute angle after the striker gave him a bump inside the box, and Bournemouth came within inches of an equaliser long before their late flurry of chances. Ederson kept out Dominic Solanke’s 67th-minute header from a devilish Tavernier corner from behind his goalline.

The first big chance fell to Haaland on nine minutes but how the striker fluffed his lines. Guardiola swivelled in disbelief and dragged his fingers down his cheeks after Haaland, clear of Marcos Senesi, fired a few yards wide from the edge of the D after being played in on goal exquisitely by Foden. Haaland, however, had a sizeable hand in City taking the lead. Mateo Kovacic scooped the ball into Haaland’s feet and the striker, off balance after wriggling goal-side of Senesi, stroked a shot goalwards with his left foot. Neto saved Haaland’s effort but Foden slotted in the rebound from close range. By this point City’s fans were enjoying themselves, reeling off the back catalogue of songs about their – increasingly noisy – neighbours. “He [Foden] has become a top-class football player,” Guardiola said. “Before he was a little boy and now he is a world-class, top player. He can play everywhere but especially in central positions he is really good.”

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There were plenty of pluses for Guardiola, with John Stones excellent and Rodri typically classy at the base of midfield. But City also had to suffer and Guardiola booted the cool box in the corner of his technical area as Bournemouth pushed for an equaliser at the end of the first half. Guardiola is eternally in pursuit of perfection but must have been comforted by the sight of Rodri, shirt tucked in, knitting attacks together in one breath and extinguishing Bournemouth attacks in another. Before City led, it was Rodri who threaded the ball through to Haaland inside Bournemouth’sthe 18-yard box but the striker declined to shoot himself and instead located Matheus Nunes, whose cutback was cleared.

Bournemouth should have levelled 10 minutes into the second half. Semenyo flew past Nathan Aké, signed from Bournemouth four years ago, and squared the ball in search of a teammate. Semenyo’s cross bounced inside the six-yard box and arrived at the feet of Tavernier, who miscued his effort, allowing Rúben Dias to head clear.

That episode should have alarmed City but a few minutes later Tavernier pulled a shot wide after Solanke superbly shielded the ball from a touch-tight Dias. Bournemouth simply would not relent. “We cannot ask much more of the players, effort-wise,” said Andoni Iraola, the Bournemouth head coach. “We were really close to getting something from the game. You have to be good inside the box against City and we weren’t good enough.”