After being unable to make a decision, judge Louis Walsh voted to go to deadlock – and that saw Carolynne Poole exit.
However, a storm raged after show boss Richard Holloway was spotted on camera whispering to Walsh, just as Carolynne, 32, was performing in the sing-off.
A furious Barlow stormed off stage and slammed the decision as "a joke".
Poole and Clark were in the bottom two and were forced into a sing-off.
Judge Nicole Scherzinger voted for Clark, whom she is mentoring, while Barlow and Tulisa Contostavlos went for Poole. Walsh was unable to make up his mind, meaning the singer with the fewest public votes had to walk.
When host Dermot O'Leary announced Poole would be leaving the show Barlow stormed off stage.
Barlow said he was "embarrassed" and criticised the judges for keeping Clark, who sang Spandau Ballet's Gold.
Clark, 32, got more votes from the public and was put through to next week's show.