Manchester City roll on to Wembley while Bournemouth’s Premier League status becomes ever more precarious. A week beginning with the court of arbitration for sport appeal victory moved to this hard-fought win for Pep Guardiola’s side before the continuation of their FA Cup defence against Arsenal. Despite a late rally, Bournemouth remain third-bottom on 31 points with two games left – one less than the other teams embroiled in the relegation battle. “It is not about performance at this stage because we want results but I can’t fault the lads,” said Eddie Howe, Bournemouth’s manager. “I’m just absolutely devastated to come away with nothing after putting so much into the game.” Guardiola acknowledged how good Bournemouth were. “We could not control them,” he said. “We struggled and their high pressing was so good so it was a difficult game.” With an eye on the FA Cup semi‑final on Saturday, Guardiola’s changes totalled six with Kevin De Bruyne and the top-scorer, Raheem Sterling, notable exclusions. Howe made four changes and decided on a 4-5-1 that had Dominic Solanke at the tip. City flooded forward from kick‑off in a move that ended with Kyle Walker’s cross going out. Guardiola had said his players just like to play and there was a pleasing moment when Ederson collected Dan Gosling’s header and hit a raking clearance straight into Gabriel Jesus. Bournemouth were turned and though Jesus’s pass for David Silva lacked accuracy the veteran playmaker’s next contribution teemed with quality. Jefferson Lerma upended the Spaniard and he stepped up to fashion a peach of a free-kick that burst past Aaron Ramsdale, cannoning in off the goal frame. City were 11-0 up on aggregate over their two previous league outings plus six minutes of the third. The score nearly increased when Fernandinho’s 20-yard shot left Ramsdale stranded before going wide. A blocked Solanke effort and a passage of play where his team hemmed City in near the centre circle signalled intent. Diego Rico was next to show: his ball from the left towards Solanke had Benjamin Mendy scrambling to clear. Bournemouth’s strategy was similar to that which rattled Manchester United recently: pace and pressing being deployed to stifle City. Junior Stanislas had opened the scoring at Old Trafford. Here he hit a free-kick at Ederson at which the Brazilian flung himself and palmed on to the left post. The ball rebounded back on to his head and out for a corner. City were now in a contest. Bernardo Silva’s scuffed attempt in front of goal was wasteful, and when Solanke turned at close range and shot only Nicolás Otamendi’s thigh prevented an equaliser. But then came a superb City second. Ilkay Gündogan fed David Silva who slid in Jesus. The No 9 nutmegged Jack Stacey, left Steve Cook in a different postcode, and smashed the ball home. City were in cruise control – for the moment. Lee Mason turned down a penalty appeal, the referee adjudging Jesus was not impeded, but Bournemouth had an Everest to climb as the second half kicked off. The introduction of Sterling for Bernardo Silva would hardly have cheered Howe’s men, while Eric García replaced Walker. The reshuffle had Jesus going left, the quiet Phil Foden right, and Sterling operating at centre-forward. Bournemouth were profligate from a corner, Rico hitting an aimless ball when his delivery came back to him. Foden’s touch from a sweeping Mendy cross was just as clumsy, the youngster normally so technically adept. Jesus was more accomplished when John Stones floated a lovely 60-yard ball into his run: the striker took it on the move but was unable to trouble Ramsdale. When Stanislas found Joshua King he finished but VAR ruled the latter was offside: it was marginal. Bournemouth were encouraged, again taking the match to City, disrupting their passing rhythm. Their best move came when Solanke passed to Stanislas who aimed a cross back at him. Ederson pushed it out to Gosling and his effort was deflected away by Gündoğan. The sense was Guardiola’s side were not yet home. They came close to being so when David Silva found Jesus, and he went down: VAR ruled no penalty. David Brooks gave City a late scare when he scored from Callum Wilson’s ball with a minute left and after the referee awarded six extra minutes, Ederson made a brave double save. “Southampton [on Sunday] is our only focus now,” Howe said.