The young centre-back had received criticism for a difficult Premier League debut in last week's 3-2 win over Wolves, but Pochettino refused to drop Foyth and he subsequently secured the spoils for Spurs in a poor match at sodden Selhurst Park.
Chances were few and far between during an unremarkable first half that was more notable for the weather than the standard of football on display.
The match opened up a little in the second half and Foyth scored his first Spurs goal, making the most of static Palace defending and consigning Roy Hodgson's men to a fifth defeat in six Premier League outings.
The host crafted the first chance of the game through former Spurs winger Andros Townsend in the 16th minute, though his effort hit the side-netting and did not worry Hugo Lloris.
Spurs struggled to create opportunities of their own, but Harry Kane did try his luck from distance just after the half-hour and forced Wayne Hennessey into a flying save.
Palace should have gone ahead early in the second half, but James Tomkins inexplicably headed a corner wide from close range.
Foyth did not make the same mistake, however, as they centre-back nodded in after Kane's initial header had been blocked 24th minutes from time.
Palace squandered its final chance late on when Alexander Sorloth blasted straight at Lloris from about eight yards, leaving Hodgson with his head in his hands as Spurs saw things out.