After sailing a little too close to the wind during their 3-2 league victory against Crystal Palace, West Ham happily accepted an afternoon free of drama. Manuel Lanzini gave them a deserved lead at the end of a drab first half and David Moyes’s side cruised from there, comfortably keeping Leeds at arm’s length and sealing their place in the fourth round of the FA Cup thanks to a professional and mature display. For Moyes, satisfaction came from seeing his side keep a first clean sheet since 12 December. Leeds kept plugging away, Jack Harrison and Dan James spurning chances to force extra time, but West Ham were rarely under siege once Lanzini’s opener had survived a VAR check for offside. Declan Rice was always in charge in midfield and Marcelo Bielsa’s defenders spent most of the contest bouncing off Michail Antonio, a barnstorming presence who was still going deep into added time, racing clear down the right to set up Jarrod Bowen’s clincher. “I want to try and go far in the Cup,” Moyes said. “We tried to go close in the Carabao Cup. We had a lot of opportunities today. On another day we might have scored more. But I’m really pleased we kept a clean sheet. Leeds cause you problems because of how they play. This is one of the toughest ties drawn out in this round.” It would have been harder had Leeds not turned up with eight key players missing. West Ham picked their strongest available side and threatened from the start, Bowen seeing a shot cleared off the line by Luke Ayling and a deflected shot from Antonio flying narrowly over. Nothing was happening at the other end. With Tyler Roberts, Patrick Bamford, Joe Gelhardt and Rodrigo unavailable in attack, Leeds were woefully short of ideas during the opening period. Sam Greenwood, a 19-year-old forward, struggled to assert himself against Craig Dawson and Issa Diop after being handed his first start by Bielsa and there was rarely any threat from Leeds before the interval, a tame curling effort from Lewis Bate summing up their toothlessness. There was no zest to Leeds, with Bate looking lightweight on his first appearance since joining from Chelsea last summer. Rice and Tomas Soucek were too strong for the 19-year-old midfielder and although West Ham rather spluttered as an attacking force at first, with Lanzini’s passing range slightly off and Antonio forced to play with his back to goal too much, there was always a sense that everything would come together sooner rather than later. So it proved when Antonio finally grabbed a chance to turn and run down the left flank after another timid Leeds attack had broken down in the 34th minute. Claret and blue shirts stormed forward in support and Antonio had time to check back before jabbing a pass towards Nikola Vlasic, who shielded the ball from Leo Hjelde before showing good upper body strength to roll away from the Leeds centre-back and advance on Illan Meslier’s goal. It was naive defending from Hjelde, who was making his debut alongside Diego Llorente. The 18-year-old was too tight to Vlasic, who was keen to make a positive impression with Saïd Benrahma away with Algeria at the Africa Cup of Nations, and he went close to conceding a penalty as he tried to slow the Croatian’s momentum. As it was, Hjelde’s challenge on Vlasic merely led to a mess, Bowen and Meslier both going for the loose ball before Junior Firpo’s desperate lunge gave Lanzini the opportunity to sweep into the empty net. The goal stood despite the officials checking whether the offside Bowen had put Meslier off – Bielsa offered no comment on the decision – and West Ham should have extended their lead before the break. Antonio blasted wide from Ben Johnson’s low cross and Ryan Fredericks finished diffidently after a lovely one-two with Bowen, who was a constant thorn in Firpo’s side. Aware that something had to change, Bielsa replaced Bate and Greenwood with Raphinha and Stuart Dallas at half-time. Yet West Ham, who visit Kidderminster in the fourth round, were still in charge. Antonio remained a menace, rumbling away from Llorente and sending Bowen through to test Meslier, and it felt like there were possibilities every time Vlasic cut in from the left. Leeds, who had moved James up front, struggled to create anything. Adam Forshaw came on for Ayling, but Bielsa’s problems increased when Firpo went down injured and had to make way for Cody Drameh. With time running out, Bielsa’s mood hardly improved when Harrison wasted a chance to equalise, somehow turning Mateusz Klich’s cross wide from close range. Leeds were toothless. James missed another inviting opening and the contest was over when Antonio, combining with Pablo Fornals, released Bowen to slide a cool finish past Meslier.