Patrick Kluivert's goal and a spate of Shay Given saves sealed Newcastle's place in the semi-finals of the FA Cup.
Kliuvert scored from eight yards after Alan Shearer had brushed off Ledley King before picking out his team-mate with five minutes gone.
Tottenham fought back, with Given brilliantly thwarting Robbie Keane then Jermain Defoe, as well as saving from Frederic Kanoute and Timothee Atouba.
Keane had a late strike ruled out for a debatable foul by Anthony Gardner.
Graeme Souness' team have now won their last seven games and will take their place in the hat for Monday's semi-final draw.
In front of an expectant crowd, Newcastle took the game to Spurs from the off, with Kieron Dyer flying past Timothee Atouba inside the opening minutes and forcing a corner.
Noureddine Naybet then made a crucial clearance, hooking the ball out for a corner, but moments later Newcastle scored.
The ball deflected fortuitously towards Shearer, who shook off King far too easily before advancing towards the byeline and cutting the ball back for the unmarked Kluivert to score.
It proved to be virtually Newcastle's only shot on target in the match.
Kluivert had the ball in the net shortly afterwards but the ball was ruled out for offside when replays suggested he was unfortunate to have been penalised.
But Tottenham rode out the storm and started to impose themselves upon the match.
Reto Ziegler smashed a long-range free-kick straight at Given, while Kanoute turned sharply and created space but again drilled his shot too close to the Newcastle keeper.
Defoe and Atouba both forced Given into action with long-range shots, while the Newcastle keeper had to hurriedly punch clear a teasing Ziegler free-kick.
And the pained expression on Souness' face told its own story when Titus Bramble limped off with a groin injury just before the break.
Souness had no defenders among his substitutes and had to call upon Jermaine Jenas to play at left-back in a rearranged back four that saw Aaron Hughes drop from midfield into the centre.
Davies snatched at a volley and dragged his shot wide as Spurs increased the tempo after the break, while King smashed the ball goalwards from a corner but his strike was blocked close to the line.
Newcastle had lost their impetus after their superb opening and were restricted to half-chances, with Robert blazing a free-kick way over the Tottenham crossbar.
And the home team had Given to thank for retaining their lead - the keeper making a brilliant double save to thwart Keane then Defoe in a matter of seconds.
As the game became more stretched Newcastle looked to be more of a threat on the break, but increasingly slipshod in defence as Spurs pushed for an equaliser.
Spurs appealed for a penalty for handball by Lee Bowyer but referee Rob Styles waved play on.
Given was called into action again, saving from Defoe, while Keane had the ball in the net but the goal was ruled out to the frustration of the Tottenham players for a foul by Gardner on Shola Ameobi.
Newcastle: Given, Carr, Bramble (Jenas 40), Boumsong, Hughes, Dyer, Bowyer, Faye, Robert (Milner 81), Shearer, Kluivert (Ameobi 68).
Subs Not Used: Harper, Butt.
Booked: Boumsong, Ameobi, Shearer.
Goals: Kluivert 5.
Tottenham: Robinson, Pamarot (Marney 80), Naybet (Gardner 88), King, Atouba (Keane 63), Ziegler, Brown, Carrick, Davies, Defoe, Kanoute.
Subs Not Used: Edman, Cerny.
Booked: Atouba, Brown, Pamarot, Ziegler, Naybet, Davies.
Ref: R Styles (Hampshire).