Nayim's spectacular goal and Neil Ruddock's first League goal for Spurs ended Liverpool's mini revival and extended Tottenham's unbeaten run to five matches in front of a near 33,000 crowd at White Hart Lane.
Both goals came in the second half after each side had missed their opportunities in the first 45 minutes but in the end Spurs were well worth their victory.
Initially, however, Liverpool had looked set for at least a point until Nayim, Spurs' Moroccan-born midfielder, unleashed a magnificent 64th minute strike for his first goal of the season that has seen him mostly on the sidelines through injury.
When skipper Gary Mabbutt, playing his first home game of the season, applied a firm header to Ruddock's long free-kick, Nayim swept in to explode a stunning volley over the head of Liverpool's million pound deputy goalkeeper David James.
And nine minutes later, after the prolific Don Hutchison spurned a golden chance to equalise for the Merseysiders, Mike Marsh crossed, and Ruddock - the man deposed as captain by Mabbutt - clinched the points with a close range header from Nayim's corner.
Ruddock, now in his second spell with Tottenham after signing from Southampton last summer, had substitute David Howells to thank for his goal, however. Howells used his first touch of the ball after replacing Dean Austin to deflect Nayim's flag kick and perfectly set up the chance from the near post.
Liverpool, again without the inflential Steve Nicol and restoring Mark Wright to the captaincy, collected three yellow cards in the first half as the sought to quell Tottenham's opening burst.
Hutchison, Mark Walters and Torben Piechnik were all booked but it was the Danish defender who created and then wasted the best chance of the first half.
He raced out of defence, took a return pass from Walters but then shot tamely at goalkeeper Erik Thorsvedt and just inside the penalty box.
A minute later, 18-year-old Nick Barmby missed an opportunity almost as good for Spurs, curling Gordon Durie's perfect pass straight into the arms of the greatful James, but the young Tottenham striker was always a handful for the Liverpool defence.
The Merseysiders suffered an extra blow when winger Walters limped off 13 minutes from the end.
Liverpool manager Graeme Souness accused his team of having their European Cup Winners' Cup match on their minds. Souness said: "In the first half we had our chances and it could have been a different story had we taken them. In the end I was very disappointed considering the way we've been playing and I can only put it down to my players thinking about Wednesday's game. We were nowhere near as competitive as we have been. Our best players were Wright and Piechnik at the back. A few egos got a knock today but all credit to Tottenham for the way they played."
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