Reading FC Women were cruelly denied a trip to Wembley and a place in the Women's FA Cup Final in sudden death of a penalty shootout.
Reading had deservedly taken the lead through Rachel Furness' bullet header early in the second half, but the Hammers levelled agaisnt the run of play with a low stabbed effort from Lehmann making it 1-1.
Reading made all the pace and looked by far the side more likely to score a winner in the final half and hour and the two periods of extra time - notably Williams missing from the spot and Furness denied by a goalline clearance. But in the end, penalties decided it and West Hem edged to victory.
The Royals began the better of the two sides, with the first meaningful shot on goal coming from the boot of Williams - Anna Moorhouse comfortably gathering in her strike from distance after a quarter of an hour.
Bartrip was in the right place at the right time to cut out a cross from the right to concede a corner soon after, Brooke Hendrix trying a speculative overhead when the set piece was floated in but not connecting properly to the Royals’ relief.
Williams watched a well-struck free kick sail just over the crossbar mid-way through the first half, while at the other end Jo Potter defended well as Leanne Kiernan looked to break into the Royals box from the left.
With game goalless and half-time approaching, Moore was quickest to react to a half-cleared dink into the West Ham box but two Hammers bodies threw themselves in the way of her stabbed shot to charge it down before Moorhouse could be troubled.
Before the break could come, Flaherty connected well with a So-Hyun corner but directed her header harmlessly over the Reading crossbar.
Half-time: Reading FC Women 0-0 West Ham United
Three minutes into the second half and the deadlock was broken when a deep free kick was hooked high back into the Hammers' boix and Rachel Furness rose highest to plant a well-directed header inside the right post for 1-0.
Bruton had a chance to add to that lead when an aerial ball over the top of the West Ham defence saw the Royals forward race through on goal. But shoulder to shoulder with the last Hammers defender she snatched at an early shot which was easy for Woodhouse to save.
But the visitors were level before the hour; the Royals failed to clear the ball from their penalty area and Alisha Lehmann stabbed a right-footed shot past Moloney at full stretch and inside the bottom right corner for 1-1.
Moorhouse came off her line to punch clear a lofted cross into the Hammers box, clattering itno Bruton but both able to dust themselves down and continue after Williams had arrowed a follow up effort wide from distance.
And Kelly Chambers' side were pressing hard to regain the lead; Potter seeing penalty appeals waved away when she seemed to be tripped inside the United box, then Williams finding Bruton in some space on the egde of the area only for her shot to be charged down.
With a little over 20 minutes of the semi-final remaining, the Royals had a glorious chance to regain the lead. Bruton battled her way into a shooting position and it was blocked by the hand of Flaherty. The referee pointed to the spot, Williams stepped up, beat the keeper but slammed her low spotkick against the left upright.
The Royals were very much on top and substitute Rakel Honnudottir headed a Williams cross just wide of the top right corner. Furness sliced a shot over the crossbar moments later.
Brave goalkeeping from Moorhouse somehow prevented Bruton who got her head to a knockdown inside the six yard box as Reading continued to impress in search of a winner. And more appeals for a penalty were dismisses as Bruton jinked her way into the area along the byline only to stumble over a stray Hammers leg.
United still posed a threat and Jane Ross glanced a header just wide from Flaherty's floated free kick. But it took a glood last gasp clearance from Longhurst to deny the Royals in the final minute of the ninety.
Six minutes of injury time were signalled and Furness was barged over in the box as Williams' corner came into the middle - again no spotkick awarded.
Williams herself had a great chance to win it moments later but she dragged her left-footed strike inches wide of the right post. And the scores remained level at full time!
Full-time: Reading FC Women 1-1 West Ham United
Reading had the first chance of extra-time, Williams breaking and finding Bruton with space to run into down the right. She cut inside and shaped to shoot, but instead was crowded out and Williams' backheel to tee up Honnudottir was halted by an offside flag.
A cross from the right bounced through to Visalli a minute later but her strike flew wide without causing Moloney too much concern. And the Royals made two changes as the first half of extra-time drew near its close - Potter and Williams repalced by Howard and Davison.
Howard was quickly into the action to thwart a chance for the lively Leon. And Davison too hit the ground running, flashing a cross-shot across the face of the West Ham goal to the gasps from the 2,334 fans at Adams Park.
Before half-time could arrive, a headed clearance off the West Ham line somehow preserved parity as Furness came close - both teams fighting hard for a place in the Women's FA Cup Final.
The second half began with another Royals attack, Honnudottir's dinked cross unable to find a blue and white hooped shirt in the middle.
Howard did well in midfield to release Bruton but excellent defending from Flaherty prevented the Royals forward from finding a shot or a pass to Honnudottir to her right.
Davison took aim next but a Hammers body charged it down as the game became stretched and tired legs desperately searched for a winner. But penalties loomed when West Ham wasted the final chance of the game, Visalli driving across goal but wide after a counter attack for the visitors.
Extra-time: Reading FC Women 1-1 West Ham United
The Women's FA Cup Semi-Final would be decided by penalties.
It started with a goal apiece. Gemma Davison scored, driving low to the left. Jane Ross levelled with a fine spotkick, aiming high to the right.
Rakel Honnudottir missed, skying her penalty over the crossbar - but Moloney produced a brilliant fingertip save to push wide Visalli's penalty. The scores 1-1.
Bruton cruelly slipped and scuffed her spotkick wide to hand the advantage to the Hammers and Leon nonchalantly sidefooted home low to Moloney's left to make it 2-1.
Furness kept hope alive with a well-struck penalty that was beyong the reach of Moorhouse and when Longhurst drove high and clipped the crossbar to send the ball flying into the stands, it was 2-2 going into the final spotkick.
Remi Allen scored in off the base of the left post to give Reading a 3-2 lead, but Flaherty found the bottom corner under real pressure to level and take the tie to sudden death.
Moore stepped up but Moorhouse got down low to her left to save. And Cho So-Hyun sent West Ham to Wembley in a cruel end for the Royals.
Reading FC Women: Moloney, Pacheco, Potter (c) (Howard 104), Bartrip, Harding, Allen, Moore, Bailey (Honnudottir 68), Williams (Davison 101), Bruton, Furness.
Subs: Jane, Pearce, Estcourt, Laws
Yellow: Potter, Harding, Moore, Bruton.
Goals: Furness 48
West Ham United: Moorhouse, Simon (Sampson 104), Hendrix, Flaherty (c), Lehmann (Kmita 118), Kiernan (Leon 59), Ross, Rafferty, Longhurst, Reichardt (Visalli 50), Cho.
Yellow: Cho, Simon.
Goals: Lehmann 56