Midfielder Klich’s poor headed clearance fell straight to Stoke’s Sam Clucas, who drilled home a low finish into the bottom right corner to give the Potters a 49th-minute lead.
United then saw Pontus Jansson sent off for a second booking after tangling with Benik Afobe with 14 minutes left and, after Luke Ayling’s header was somehow kept out by Jack Butland, Stoke netted a second when Joe Allen slid home at the far post with two minutes to go.
Leeds pulled a goal back in the fifth minute of stoppage-time through Ezgjan Alioski’s low strike from Pablo Hernandez’s corner, but it was too little too late as the Championship leaders squandered the opportunity to extend the gap back to third-placed Sheffield United.
Saturday’s contest at the bet365 Stadium was also played out against the backdrop of more developments in the controversy surrounding head coach Marcelo Bielsa’s admission that he sent a member of staff to watch Derby County train before the clubs’ meeting at Elland Road 11 days ago.
Bielsa revealed last week that Leeds had spied on training sessions of every Championship club this season, a comment that prompted 11 sides in the division to write to the English Football League to demand a detailed investigation into his methods.
The EFL and FA are both investigating the matter while on the field Leeds have picked up just three points from the last 12 available. But Klich insisted he is unconcerned by the slump and is backing Leeds to rediscover their best and claim a place in the Premier League over the remaining 18 games. “We’re not worried,” said Klich.
“We lost the game, but we dominated and we created, maybe not clear chances but opportunities to score a goal.
“We know we can do better and score goals, but it’s a difficult league. There are no easy games and other teams are dropping points. It’s not easy, but we’re going to fight until the end and we’re very optimistic.
“Stoke played very defensive, very good and organised. They were waiting for us in their half and it was very difficult for us to create anything, especially when we lost a goal after our mistake and my poor clearance.
“It wasn’t a good afternoon for us. Everyone knows what we need to do and everyone is focused on the games.”
Stoke City: Butland, Bauer, Allen, Williams, Etebo, Afobe, Martins Indi, Adam, Shawcross, Clucas, Campbell (McClean 67). Unused substitutes: Federici, Ince, Berahino, Crouch, Edwards, Woods.
Leeds United: Peacock-Farrell, Ayling, Jansson, Cooper, Alioski, Forshaw, Clarke, Klich (Stevens 76), Hernandez, Harrison (Roberts 61), Roofe. Unused substitutes: Casilla, Davis, Shackleton, Stevens, Halme, Gotts, Roberts.
Referee: Gavin Ward (Surrey).