Spurs' struggles in the final third continued on Sunday, with a home blank denying them the opportunity to close on the Premier League leaders.
Newcastle - who saw off Chelsea last weekend - took just 13 minutes to settle the contest at White Hart Lane, with Yoan Gouffran robbing Paulinho of possession in midfield and rolling a perfect pass into the path of Remy to round Brad Friedel and stroke into an unguarded net.
The second half saw Spurs lay siege on the Magpies goal in pursuit of a leveller, but they found Tim Krul in inspired form - with the Dutch keeper pulling off a string of fine saves to leave the hosts frustrated.
The first chance for the home side came from a ninth-minute corner, which was headed over by Soldado when he should have done better.
The opening seemed to stir Newcastle into life as Remy had a sight of goal shortly afterwards, but Tottenham defender Vlad Chiriches was on hand to block the France forward's shot behind for a corner.
Friedel just about dealt with the resultant set-piece and then had to push Yohan Cabaye's effort behind as the visitors came into the match.
But Friedel could do nothing about Remy's strike moments later as Gouffran robbed Paulinho of possession and played a through-ball to the QPR loanee, who took the ball around the American goalkeeper and slotted home.
Spurs chased an instant response but no-one could get on the end of an inviting Christian Eriksen cross and Paulinho blazed over as a quick equaliser eluded them.
Roberto Soldado forced Krul into a full-stretch save as his flicked header from Eriksen's free-kick sent the goalkeeper flying high to his right.
Eriksen stung the palms of Krul with a powerful long-range effort, with the early afternoon sunshine making the save less routine.
Shola Ameobi had the ball in the back of the net after 37 minutes but he had been flagged offside as Newcastle adjusted to a counter-attacking approach.
Spurs were inching closer and closer to an equaliser but were yet again thwarted by wonderful goalkeeping from Krul. This time the Holland international flung himself across goal to tip Paulinho's curling shot away from goal.
Chiriches did not see out the half for Spurs after the defender was left with a bloody nose as he challenged for a high ball inside the Newcastle penalty area.
The second half followed on from where the first had ended, with Krul again denying everything thrown at him by Spurs, using his legs to keep out Eriksen's stab towards goal.
A deflected Sigurdsson free-kick again brought out the best out of Krul, who was sharp enough to block Younes Kaboul's follow-up with Mapou Yanga-Mbiwa then clearing ahead of the onrushing Tottenham cavalry.
Newcastle showed they were still a threat at the other end as they broke forward through Moussa Sissoko, whose shot was pushed away by Friedel.
Jermain Defoe was introduced with 22 minutes remaining as Villas-Boas decided to play with two forwards, Sigurdsson making way.
Andros Townsend cut in and arrowed a shot towards goal which Krul could only push away this time, but he got enough on the ball to keep it out of the path of the fast-approaching Soldado.
Brazil midfielder Paulinho hit straight at Krul when well-placed inside the penalty area as time started to run out for the home side.
Even when Spurs did manage to beat Krul they found the woodwork blocking their path as Jan Vertonghen's back-post header hit the crossbar, ensuring that a goalkeeper on the pitch rather than one playing no part - with Hugo Lloris absent from the Spurs squad - took at least a share of the headlines.