Southampton always looked dangerous and equalised when Dusan Tadic controlled the ball deftly to set up Davies who flicked the ball home from close range after 31 minutes at White Hart Lane.
The same combination provided Saints' winner halfway through the second half when Davies played a neat one-two with Tadic on the edge of the box and scored with a low shot that beat Hugo Lloris in his bottom corner.
Southampton climbed into sixth place, still in the hunt for a Europa League slot, while Spurs stayed second, two points ahead of arch-rivals Arsenal with one game left.
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"We are still in a great position and if we look back to the start of the season we all should be proud," Spurs manager Mauricio Pochettino said.
"We need to look at ourselves, not at our neighbour (Arsenal). We need to think like a big club, not worrying about what's happening in another house. We need to change that mentality, to be strong, to be a big club."
Southampton manager Ronald Koeman was delighted with his side.
"If we can win next week at home we will have 63 points -- a really fantastic achievement by the team. We like to play in Europe, and it's important for the clubs and the players."
(Reporting by Neil Robinson, editing by Ed Osmond)
