Niko Kranjcar and Vedran Corluka scored their first goals for Tottenham as they twice came from behind to ensure Bolton are still without a home league win.
Just three minutes were on the clock when Ricardo Gardner put Bolton ahead from close range, but Kranjcar slammed in Peter Crouch's knockdown to level. Kevin Davies deservedly restored the hosts' lead following a flowing move.
However, Corluka headed in a corner to make it 2-2 and though both teams had chances, neither were able to win it. A point apiece was probably just about the right result from a topsy-turvy game, though Bolton will feel their first-half dominance alone should have brought them all three.
Gary Megson's side can comfort themselves with the knowledge that the result stretches their unbeaten run to five matches, though, while Tottenham will be happy to have grabbed a point at a ground where they have never won.
It concluded a strange week for Redknapp, who was forced to deny bizarre stories he was about to quit as Tottenham boss after bookmakers had slashed the odds on him leaving White Hart Lane from 50-1 to evens.
And his mood was not helped early in the match when Bolton - who had scored all eight of their league goals from broken play this season before this game took just three minutes to underline their threat from set-plays.
Spurs failed to deal with a long throw into the box and Gardner pounced on Carlo Cudicini's spill from Chung Yong Lee's shot to slam in the opener. Some would say it was a 'typical' Bolton goal - direct and uncomplicated - but the Trotters are all too often regarded as one-dimensional and at times their football in the first half left Tottenham chasing shadows.
In truth, the hosts could have scored five by half-time. Tamir Cohen was twice set free in the box only to scuff his shot on goal, while Kevin Davies and Matthew Taylor also had close-range efforts smothered well by the otherwise erratic Cudicini.
And yet they entered the break level. Kranjcar was the poacher extraordinaire, the Croatian slamming home with aplomb from Peter Crouch's knock-down 16 yards out for his first Spurs goal in the visitors' first attack of note.
Something needed to change for Tottenham and while they continued to look vulnerable under the high ball in defence, they were at least more of a threat in attack in the second half.
Aaron Lennon in particular came into his own and he forced a smart save on the stretch from Jussi Jaaskelainen with a left-footed curler, while Crouch drove narrowly over from just inside the box minutes later. But Spurs could do little to prevent the Trotters regaining the lead with a wonderful move.
Cohen was again at the heart of it, the midfielder collecting Lee's back-heel and dinking to the far post for Davies to head in from a narrow angle. Again Tottenham responded, Jaaskelainen somehow deflecting Crouch's goalbound effort on to the bar just moments before Corluka looped a precise header into the far corner from Kranjcar's corner.
In a frantic finale, both teams went for the win, with Cudicini pushing Taylor's goalbound header round the post and Jaaskelainen again denying Crouch when the tall frontman looked primed to grab the winner.
But neither side could find a breakthrough and the match ended in a draw, a result that temporarily at least lifts Tottenham into third in the Premier League and Bolton into 12th.
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