Strachan named an unchanged team, with Paul Telfer continuing his good form in the centre of the park.
Spurs had a shot in the opening seconds of the match, Dalamt's effort going well wide of Paul Jones' goal. Jones is still pipping Antii Niemi for the 'keeper's jersey, with a series of fine performances.
Saints first effort was equally wide, but Matt Oakley's corner reached James Beattie in the middle. The England international made a determined jump to reach the ball and put it into the net for a great early opener. The Tottenham support went very quiet as the prospect of yet another defeat seemed likely.
In contrast the full Saints contingent, willed their team on to continue their unbeaten run.
The Spurs players showed a will to get back into the game, Freddie Kanoute heading onto the top of the bar from a Rohan Ricketts cross.
With Saints midfield having looked very solid in recent weeks, Spurs opted to pump long balls into Kanote and to focus on the flanks. Saints defence looked confident and capable of withstanding anything that SPurs could throw at them.
Saints began to dictate the pace of the game, with Oakley, Le Saux and Phillips putting pressure on the home side. Matt Oakley and Fabrice Fernandes put long range efforts well wide, but the Saints managed to keep the game at their pace.
Kanoute remained a danger for Spurs but Svensson and Lundekvam prevented him getting any clear cut opportunities. Chances were few for the remainder of the half, the home side claims for a hand ball by Lundekvam ignored by the referee.
Stephen Carr worked hard, not only to keep Saints from getting a second, but to get his side on level terms. His good run at Graeme Le Saux resulted in a powerful shot which went into the side netting.
Kevin Phillips hit back from Saint, his low effort going just wide of Kasey Kellar's goal.
On forty two minutes, Saints inflicted a hammer blow to Spurs chances of getting into the match. James Beattie's right footed free kick, looped over the wall and into the top right of Kellar's net.
Saints had looked comfortable with only a one goal lead, but there is always the chance of an equaliser. At two nil, Spurs never looked likely to get back into the game.
A powerful shot from Bobby Zamorra before the break was well saved by Paul Jones, who also dealt well with the resulting corner.
In a bid to turn things round in the second half, Glenn Hoddle took off his most influential player of the firs period and brought on Darren Anderton. Bobby Zamora also came off, after a frustrating half to be replaced by Robbie Keane.
Despite the changes, it was Saints who almost got a third, Fabrice Fernandes sending an excellent ball in to Kevin Phillips, who couldn't convert it from eight yards out.
Kasey Kellar also had to stop a powerful left footed strike from Graeme Le Saux, as Saints continued to control the match.
Le Saux continued to pressurise the now lack lustre Spurs defence. His excellent cross resulted in a third for Saints as Kevin Phillips glanced the ball into the net at the near post. Phillips was well rewarded for yet another excellent game full of running and creativity.
As their fans continued to leave, Spurs struck back as Kanoute put the ball in from close range from Robbie Keane's cross. Saints, who haven't conceded since the opening game, were caught too far forward after a corner kick, and will no doubt face some harsh words from Gordon Strachan.
With one goal back, Spurs tried to get themselves back into the game with half an hour remaining. Saints handled the Spurs pressure well seeing off an effort from Kanoute and a header from Dean Richards.
Strachan brought on Anders Svensson for Fabrice Fernandes, in order to hold up the ball in midfield. Spurs continued to sense they still had a chance of getting something from the game, Jones saving well from Postiga's right footed volley.
Saints had a chance to put themselves out of Spurs's reach. Kevin Phillips found himself through on goal. He rounded Kellar and his shot came off Stephen Carr's knee and hit the bar.
With five minutes left, Chris Marsden came off for David Prutton. Prutton, unused to playing on the left flank is still a midfielder in Chris Marsden's mold and Saints continued to shut Spurs out.
Spurs last chance fell to Ricketts who chipped Paul Jones only for the ball to go over the bar.
In the end, Spur's single goal was nothing but a consolation and Saints fully deserved their win. It was an impressive victory with the back four working very well together as always. We controlled the midfield and Phillips and Beattie were both on the score sheet.
Once again, there can't really be any complaints despite a few worrying minutes after Spurs got their first as Saints found themselves on the defensive.
Strachan's great term in charge continues, a position that he wouldn't have got had it not been for Hoddle's delusions of grandeur. The boos form the Spurs fans at the final whistle should have brought him back down to earth with a bump and his future must now be in doubt.