Benoit Assou-Ekotto and Louis Saha struck inside the first six minutes before Saha's second and a strike from Niko Krancjar ensured the home side reached the interval with a four-goal advantage.
Emmanuel Adebayor then completed the scoring midway through the second half as Spurs moved 10 points clear of fourth-placed Arsenal.
For Redknapp, this was the perfect end to a week in which he was cleared of charges of tax evasion and been installed as the clear favourite to succeed Fabio Capello as England manager.
The manager had described the stresses of his two-week court ordeal in the build-up to this game.
He also admitted to being flattered at being linked with the England job, although added it would be a wrench to leave Tottenham.
The reaction of the Spurs supporters will have done nothing to change that, with the home fans making it clear they would like the manager to remain at the club.
Both matters were cast to one side as he switched his focus back on to Tottenham and their continuing efforts to increase the pressure on Manchester United and Manchester City at the head of the table.
Chelsea's defeat at Everton earlier in the day also meant Spurs could extend the gap between themselves and fourth place.
And they were given the perfect start when they raced into a two-goal lead inside the first six minutes.
If Redknapp was looking for an antidote to the off-field affairs that have dominated his week, then this was the ideal response from his players.
Their intent was clear from the moment Adebayor exchanged passes with Kranjcar on the edge of the Newcastle area before delivering a low cross towards Assou-Ekotto who slotted the ball into an empty net.
Two minutes later, and Newcastle were again carved open by Adebayor who this time picked out Saha with a deep, right wing cross.
The former Everton striker was making his full debut after joining Spurs on transfer deadline day and he ensured it was an occasion to remember by finishing with a left foot volley.
Tottenham were rampant while Newcastle simply looked shell-shocked.
It could have got worse for the visitors in the 15th minute when Kranjcar shot over when he should have done much better.
But that turned out to be only a temporary reprieve and four minutes later, Saha made it three when he drilled a shot past Tim Krul after Adebayor had laid off Luka Modric's cross.
The visitors finally threatened Brad Friedel's goal when Demba Ba sent a free kick flying narrowly wide.
That proved to be a rare moment of activity in the Spurs goalmouth and Redknapp's side established a four-goal lead in the 33rd minute.
Once again Adebayor was involved, firing in a shot after collecting a pass from Saha and Kranjcar followed up to convert the rebound after Krul had saved.
Redknapp's reaction to each goal had got progressively more animated and this time he virtually danced along the touchline in celebration.
Newcastle had no answer and after avoiding further setbacks before the break, were then left with the task of avoiding more humiliation after the restart.
They held out for 20 minutes, but eventually wilted when Saha turned provider and nodded down for Adebayor who volleyed home for the fifth.
Source: AFP
Source: AFP