Redknapp, who was cleared of tax evasion charges on Wednesday and was immediately installed as favourite to succeed Fabio Capello as England manager, saw his team race into a two-goal lead after five minutes courtesy of goals from Benoit Assou-Ekotto and Saha.
Saha, making his first Spurs start, scored his second in the 20th minute before Niko Kranjcar and Emmanuel Adebayor completed the rout.
Man Utd returned to the top of the Premier League with a 2-1 lunchtime win over Liverpool.
However, the match at Old Trafford was overshadowed by Luis Suarez's refusal to shake hands with Patrice Evra, the player whom he was found guilty of racially abusing in October which led to an eight-match ban.
Wayne Rooney scored twice early in the second half and although Suarez pulled one back with 10 minutes remaining United held on to move ahead of Manchester City, who play on Sunday.
Chelsea lost their grip on fourth place after a 2-0 defeat against Everton at Goodison Park.
Toffees midfielder Steven Pienaar, who returned on loan last month, did parent club Spurs a favour by scoring in the fifth minute for his first league goal since September 2011.
Fellow on-loan player Denis Stracqualursi hit his first Premier League goal in the 71st minute to wrap up the points and extend Chelsea's poor run to just 12 points out of the last 30 available.
Arsenal took advantage to move into the final Champions League qualification spot as they came from behind to beat Sunderland 2-1.
Having gone behind to James McLean's 71st-minute goal, Aaron Ramsey equalised with a shot off both posts just four minutes later.
And Thierry Henry's last-minute goal, converting Andrey Arshavin's cross, nicked the three points and took them above Chelsea on goals scored.
At the other end of the table Wigan did their survival chances the world of good with a 2-1 derby win over fellow strugglers Bolton.
The Latics began the day five points from safety but ended just two behind 16th place.
Just before half-time captain Gary Caldwell powered home a close-range header, only for Mark Davies to smash home a left-footed drive against the run of play in the 67th minute.
However, with 14 minutes remaining James McArthur capitalised on Victor Moses' shot which rebounded back off goalkeeper Adam Bogdan to poke home the winner.
Fellow strugglers Blackburn held off a late rally from QPR to win 3-2 but the concession of those goals prevented them moving out of the bottom three.
Striker Ayegbeni Yakubu, returning from a three-match ban, scored his 14th goal of the season, midfielder Steven Nzonzi drove home his first since August 2010 and Nedum Onuoha's own goal put Rovers 3-0 up at the break.
Jamie Mackie scored twice in the last 19 minutes, the second a brilliant strike in injury time, but they could not force a draw.
Deadline-day signing Pavel Pogrebnyak scored on his Fulham debut with a 16th-minute effort as his side beat Stoke 2-1.
Clint Dempsey's 35-yard shot cannoned down off the crossbar and hit goalkeeper Thomas Sorensen on the back to make it 2-0 and Ryan Shawcross 78th-minute header from Jermaine Pennant's corner proved nothing more than a consolation.
Norwich came from behind to beat hosts Swansea 3-2.
Danny Graham's 23rd-minute goal put Swansea ahead but two goals for Grant Holt, either side of one from Anthony Pilkington, gave the visitors a cushion which they needed when Graham's 87th-minute penalty set up a frantic finish.
Source: FOOTYMAD
