Pochettino made no changes at the break but he must have had some choice words for his players, who had barely been able to string two passes together.
But the pattern was the same, and Pochettino looked more and more worried as he stood, arms folded, in his technical area to see Aaron Cresswell head another Payet cross over the bar.
Then it was heart in mouth time for Hammers keeper Adrian, who could only parry Toby Alderweireld’s shot right into the path of Harry Kane.
But Kouyate saved his bacon by nipping in quick to clear just as Kane, who was only four yards out, looked certain to score. Kane, stretching, missed another chance moments later.
Pochettino eventually went for it, throwing on first Alli, then Heung-Min Son, and then midfielder Tom Carroll for defender Wimmer. But they never truly threatened an equaliser.