The Real Madrid midfielder slotted the ball into the bottom-right-hand corner, with what was the first goal of the game.
Hugo Lloris may feel as though he should have done better - the Tottenham captain got a strong hand to the ball, but he could only divert it further into the corner.
The penalty was given when Leroy Sane attempted to put a low cross into the French penalty area.
However, he found his path blocked by Kimpembe, who was adjudged to have his hand in an unnatural position.
Kroos duly stepped up to slot home the penalty, albeit in unconvincing fashion.