Following a week which saw Redknapp cleared of tax evasion charges and then installed as the bookmakers' favourite following the resignation of England boss Fabio Capello, Redknapp was relieved to get back to the game.
Following a 13-day stint in court he was able to watch Louis Saha, with a double, Benoit Assou-Ekotto, Niko Kranjcar and Emmanuel Adebayor score the goals to down Alan Pardew's men and keep Spurs in the title race.
Redknapp said: "The crowd have been brilliant with me, they've been great and I appreciated their support.
"This was the most difficult week I've ever had. I wouldn't want anyone to go through that and what it's done to my family was worse.
"But it's behind us now and the week's turned out good."
Pardew said: "Tottenham were irresistible. Some of the things they were doing, they were doing for fun, Adebayor and Saha were a real handful for us.
"They had an extra bounce in their step after what happened to their manager this week.
"They all wanted to show they wanted their manager to stay but we should have done better for the first two goals."
The win kept Tottenham in contention with the top two on a day when Manchester United's 2-1 win over Liverpool at Old Trafford was overshadowed by the continued fallout from Luis Suarez's spat with Patrice Evra.
Suarez's first start following his eight-game ban for racially abusing Evra was marred by a new flashpoint when he refused to shake Evra's hand before the game - an action for which the player and his club subsequently apologised.
As both managers continued to put their case on TV after the game, United were celebrating a Wayne Rooney double which earned them a win despite Suarez's late consolation.
Chelsea manager Andre Villas-Boas accepted the negative chants of his own club's supporters after the 2-0 defeat at Everton left them fifth in the table.
Villas-Boas, whose position at Stamford Bridge is coming under scrutiny, said: "It is part of the job. At the moment we are sitting fifth in the league and it is not enough for us."
Everton manager David Moyes saw Steven Pienaar and Denis Stracqualursi get the goals and then praised the former, who is back at Goodison Park on loan from Tottenham.
Moyes said: "He got clapped by everyone at the end, some of the stuff he did was terrific.
"I said to him at the end it was like he had never been away. Sometimes clubs just fit players and maybe that is the case."
Arsenal manager Arsene Wenger enjoyed the "luxury" of Thierry Henry after the striker scored the winner in the 2-1 victory at Sunderland.
"It's just a luxury to have a player like him on the bench," said Wenger.
Henry, playing in the final Premier League game of his loan spell at the Gunners from New York Red Bulls, hit the late winner.
James McClean had given Sunderland the lead before Aaron Ramsey struck the equaliser.
Strikes by Aiyegbeni Yakubu and Steven Nzonzi and a Nedum Onuoha own goal saw Blackburn to a 3-2 home win against QPR. Jamie Mackie scored twice late on for the visitors.
Strugglers Wigan earned a 2-1 win at Bolton with goals from Gary Caldwell and James McArthur, Mark Davies netting for the home side.
Pavel Pogrebnyak scored on his Fulham debut in the 2-1 win over Stoke. Clint Dempsey's shot came back off the bar and hit Stoke keeper Thomas Sorensen on the back before the ball crossed the line, while Ryan Shawcross headed a consolation for the visitors.
Grant Holt scored twice and Anthony Pilkington also netted as Norwich won 3-2 at Swansea, Danny Graham getting two for the home side.