Scott Sinclair's late goal earned the Swans a deserved point against in-form Spurs.
The home side created the best chances of an even first half, but it was the visitors who went into the break in the lead after Rafael Van der Vaart turned home Benoit Assou-Ekotto's low cross.
But the Swans turned in an impressive second half showing as they pushed the visitors back for long periods, and they could have levelled when Luke Moore saw his effort tipped round the post by Brad Friedel.
However, Brendan Rodgers' side did earn a share of the spoils with minutes to play, as Angel Rangel's cross deflected off Walker and bobbled to Sinclair at the far post who turned the ball home.
With a trip to Aston Villa to come on Monday, Swans boss Brendan Rodgers shuffled his pack against the league's high-flyers.
There were six changes in total. Neil Taylor returned at left-back after missing the draw with QPR with a knee injury. It meant young Jazz Richards, who has impressed in recent weeks, switched from the left to right-back in place of the injured Angel Rangel (ankle).
Skipper Garry Monk returned to partner Ashley Williams in place of central defender Steven Caulker whose loan agreement with Spurs prevented him from facing his parent club.
In midfield, former Spurs player Mark Gower came in for Leon Britton, while Stephen Dobbie started his first game since the opening fixture at Manchester City. He replaced Kemi Agustien, with Joe Allen making up the central trio.
Up front, Nathan Dyer came in for Wayne Routledge on the right wing, while Luke Moore replaced Danny Graham as the central striker. Scott Sinclair remained on the left.
Redknapp was still without the services of Aaron Lennon (hamstring) and Ledley King (knee), but Jermain Defoe made the bench following injury.
Swans: Vorm, Williams, Taylor, Sinclair, Dyer, Dobbie, Monk ©, Moore (Graham, 68), Allen, Gower (Agustien, 62), Richards (Rangel, 45)
Subs: Britton, Graham, Routledge, Lita, Rangel, Tremmel, Agustien
Spurs: Friedel, Bale, Kaboul, Parker © (Livermore, 71), Adebayor, van der Vaart (Defoe, 71), Gallas, Modric, Walker, Sandro, Assou-Ekotto
Subs: Defoe, Dawson, Kranjear, Cudicini, Rose, Livermore, Pienaar
Referee: Phil Dowd
Following Manchester United's defeat to Blackburn earlier in the day, Spurs were looking to close the gap at the top of the Premier League table, but it was the Swans who made the brighter start and created the game's first chance after just five minutes.
The returning Nathan Dyer skipped round the challenge of Assou-Ekotto on the right flank and as the winger cut inside he curled a delightful left foot shot that Brad Friedel tipped round the post at full stretch.
Shortly after, Stephen Dobbie shot straight at Friedel from 20 yards before Spurs had their first effort on goal after 14 minutes when Luka Modric shot wide of Michel Vorm's left hand post from just outside the box.
And as the Swans continued to make all the running, they were a whisker away from taking the lead when Luke Moore surged forward and squared the ball across the box to Scott Sinclair, whose right footed effort curled inches wide of Friedel's right hand upright.
However, the home side nearly came unstuck when Dyer's weak backpass let in Emmanuel Adebayor, but Michel Vorm came racing out of his goal to tackle the striker and clear the danger.
From the resulting corner, Sandro drilled wide from the edge of the box and Adebayor curled an effort wide of Vorm's goal as Spurs had their best spell of the first half.
But for all the home side's chances, it was the visitors who took the lead momentsbefore the half time break.
Assou-Ekotto outpaced Jazz Richards down the left flank and after his low cross bobbled around the Swans penalty area, it fell to Rafael Van der Vaart who lashed the ball past Vorm from six yards.
Half time: Swans 0 Spurs 1
Brendan Rodgers made one change at the break, as Jazz Richards made way for Angel Rangel.
And it was the visitors who made a bright start in the second period, Kaboul linking up well with Adebayor before firing straight at Vorm before the Togo international connected with Bale's cross but he turned his effort just wide.
But the home side responded well and created a chance of their own after a neat move, as Luke Moore connected with Rangel's right wing cross but the striker could only head wide.
On 55 minutes Spurs nearly doubled their advantage after a swift counter attack. Adebayor turned away from the Swans defence and with Van der Vaart racing up in support, he played in the Dutchman but he saw his curling shot tipped round the post by Vorm.
On 62 minutes the home side made their second change of the afternoon as Kemy Agustien replaced Mark Gower for the third game in succession as the Swans looked for a route back in to the game.
Just four minutes later and Swansea had two great chances in which to haul themselves level. First, Luke Moore produced a sublime piece of skill to wriggle free of two Spurs defenders before he saw his shot tipped round the post by Friedel.
And from the resulting corner, substitute Angel Rangel saw his powerful volley flash a fraction wide of the far post to lift the home crowd.
The Swans then introduced top scorer Danny Graham for Luke Moore, while Spurs made double substitution of their own when Parker and Van der Vaart were withdrawn for Jake Livermore and the returning Jermain Defoe.
And it was Swansea's record signing that had a golden chance to level the scores after 76 minutes when he connected with Scott Sinclair's strike, but he saw his header drift inches wide of Friedel's right hand post.
The home side continued to pile on the pressure as Dobbie's low cross was hacked behind by Kyle Walker, and from the following corner, Joe Allen's low drive was cleared off the line by Modric.
While at the other end, Vorm did well again to save from Adebayor at his near post but the Swans drew level with a well deserved goal on 85 minutes when Rangel's deflected cross found its way to the unmarked Sinclair at the far post who turned the ball into an empty net.
As the fourth official signalled three minutes of added time, Gareth Bale lined up a free kick outside the box that was comfortably saved by Vorm as the Swans held on to earn a valuable point.