A double in either half from the in‑form England striker Fran Kirby at home to Manchester City booked Chelsea a place in the FA Cup final.

“That’s what she does best,” her manager Emma Hayes said of the player who scored once again in the knockout competition. “She’s great in the FA Cup. She’s really got a lot of big semi-final goals for this team. We’ve had to nurture her through the week, I didn’t think she was going to play today but that’s how tough she is and how much she wants to put it on the line.”

Chelsea took full advantage of any weary England legs in the Manchester City starting 11 as Kirby fired them in front inside five minutes. Eight Manchester City players featured over England’s two World Cup qualifiers against Wales and then Bosnia-Herzegovina, compared to Chelsea’s two. With Kirby sitting out the trip to Sarajevo to protect a hamstring niggle the London club clearly benefited from more rested legs.

The England and City captain, Steph Houghton, was at fault when she mistimed a headed clearance to let in Kirby who slotted past the 18-year-old Ellie Roebuck.

Going a goal behind failed to rattle City who dominated possession for the rest of the half but were unable to break through a resilient Chelsea back line. While wave after wave of City attack arrived, Nadia Nadim was closed out by Millie Bright and Maren Mjelde and looked isolated in the middle. City’s brightest outlet looked to be Nikita Parris down the left, but bar a shot from distance and a through balled poked straight at Hedvig Lindahl there was little direct threat on the Chelsea goal.

With two league meetings unable to separate the sides this season, this FA Cup semi-final match-up was the first chance to see these side go head to head and be forced to fight for a win.

Chelsea were missing Ji So-yun, who is in Jordan with South Korea for the Asia Cup, and Ramona Bachmann was ruled out late on, leaving them with just four on the bench, but they showed no signs of being fazed by the rearranged starting XI as 19-year-old Erin Cuthbert stepped in and provided the assist for Kirby’s second. Both sides have shown signs of fatigue though.

A heavy fixture schedule – both are in the semi-finals of the Champions League – has seen their league form take a hit. City have lost two and drawn one (against Chelsea) since they last won a WSL match against Liverpool on 11 February. Chelsea have had three draws in a row since they last picked up three points – away to Yeovil on 21 February. Both managers were critical of the fixture pile-up.

“We’re down to our bare bones, but it was so gutsy from the team,” Hayes said. “You can see why I’ve complained about the gruelling schedule. Because for both sides, you see injuries mounting and that’s what starts to happen when you’ve got back-to-back games. You can probably see now why it’s a tall order for an English side to go all the way in the Champions League.”

Cushing said: “Myself and Emma are in the same situation. We want to get the players on the training pitch but we don’t get the opportunity.”

Chelsea started the second half much more brightly and the game started to open up. Drew Spence forced a save from Roebuck who spilled the ball before falling on it under pressure. A lengthy stoppage as Maria Thorisdottir was carried off with an ankle injury showed no signs of slowing play as City began to knock on the Chelsea door, Georgia Stanway forcing a fingertip save from Lindahl. But pushing forward left them exposed, and again Kirby was there to pounce and score her 22nd goal of the season.

Capitalising on another City mistake, this time from Jen Beattie, Kirby pick the ball up near the halfway line and drove towards the City area before cutting inside and slotting a cool finish past Roebuck in the 74th minute.

A standing ovation greeted the striker as she made way for Aluko shortly afterwards, rested, no doubt, for Chelsea’s midweek trip to Everton and then Sunday’s visit of Wolfsburg, who have twice knocked the London side out of the Champions League.

City, meanwhile, who started the season with hopes of multiple silverware, now look like they could finish the season empty-handed. Nick Cushing’s side will have to dust themselves off ahead of a visit from Sunderland before they host the Champions League holders, Lyon, at the Academy Stadium next weekend.

Chelsea will play Arsenal in the FA Cup final at Wembley on 5 May.

PFA Player of the Year shortlists announced

Women’s PFA Player of the Year shortlist: Fran Kirby (Chelsea), Jill Scott (Manchester City), Ji So-Yun (Chelsea), Maren Mjelde (Chelsea), Millie Bright (Chelsea), Ramona Bachman (Chelsea)

Young Player of the Year shortlist: Ellie Roebuck (Manchester City), Erin Cuthbert (Chelsea), Gabby George (Everton), Georgia Stanway (Manchester City), Lauren Hemp (Bristol City), Keira Walsh (Manchester City)