Going into the game West Brom had kept just one clean sheet in their eight Premiership away games so far in this campaign. Any possibility of improving that record disappeared with only one minute on the clock.
Teddy Sheringham was manhandled yards outside the area and West Brom employed a confusing defensive system to deal with the potential threat of a free-kick from either Ziege, Redknapp or Anderton.
It was Ziege who spotted the gap between the wall and Russell Hoult's right hand post and curled his low effort accordingly to give Spurs the perfect start.
Glenn sent out a very attack-minded line-up, with a midfield featuring the returning Redknapp and Davies alongside Darren Anderton. Gus Poyet reverted to the bench and there was no place for Steffen Freund. Chris Perry stepped in for the suspended Goran Bunjevcevic in the central defence.
A goal down and few minutes into the game, West Brom composed themselves and offered a considerable attacking threat of their own and had Spurs overrun at times.
From a break down the right Lee Hughes flashed the ball across the goal and both Jason Roberts and Andy Johnson failed to apply the finishing touch. Three minutes later Roberts rounded Kasey Keller to the left of his area, but the angle worked against the Baggies striker.
On 14 minutes the visitors really should have been level when the lively wing-back Neil Clement missed an open goal after great work by Roberts and Sigurdsson and, shortly after, Keller pulled off a fine save to deny Jason Koumas.
Despite almost dominating the game, West Brom found themselves two goals down after 30 minutes. A brilliant piece of interchange between Teddy Sheringham and Ziege led to the German dispatching a superb lofted through ball into the path of Keane, who dinked the ball past Hoult with great confidence for his sixth Premiership goal of the season.
It was nearly all over just before the break when Keane found himself in the clear again, but this time the elbow of Hoult diverted the ball over the bar.
Spurs were slightly more fluid in the opening stages of the second period, but West Brom against put us under pressure and Glenn introduced Steffen Iversen to the action on 64 minutes and altered the system by withdrawing Ledley King and reverting to a back four.
There was a scare on 64 minutes when substitute Scott Dobie broke through and was felled by Keller just outside the area. Thankfully the referee only saw fit to show yellow. Kasey responded excellently to the resulting free-kick by saving low to his right from a Koumas' piledriver.
West Brom extracted some reward for their efforts on 72 minutes Dobie picked up the ball down the right and let fly with a shot that bounced across Keller and landed in the bottom right hand corner to make it 2-1 and ensure a nervy end to the game.
Gus Poyet came off the bench in place of Sheringham in order to stiffen the midfield but, minutes after, West Brom nearly levelled when Clement headed just wide from a Koumas corner.
Eleven minutes from the end, nerves were settled and the game was won when Poyet applied the finishing touch following a goalmouth scramble.
Dean Richards headed a Stephen Carr throw into the danger area and Iversen tangled with three defenders and managed to put in a shot that Hoult did well to save. The ball came back out and Poyet just squeezed a shot that evaded the West Brom rearguard and trickled over the line without any help from the onlooking Keane.
MINUTE BY MINUTE GUIDE TO THE ACTION (press refresh for regular updates)
2mins: GOAL. Free-kick won by Sheringham perfectly executed by Ziege, curled low from 25 yards into the slightest of gaps into the bottom corner. 1-0.
8mins: Hughes whipped in cross from right-hand side, Roberts didn't connect with attempted flick and Johnson, sliding in, just inches away from the ball at far post.
10mins: Roberts burst through, Keller out quickly, Roberts around him but forced wide by the challenge and angle too tight for him.
14mins: CHANCE. Roberts released Balis down the right, low cross found Clement joining in from left back, golden chance, six yards out, struck wide of empty net.
18mins: Koumas dribbled past four defenders, slipped ball to Hughes, weak finish straight at Keller from 10 yards.
27mins: SAVE. Keller at full stretch to deny Koumas from 25 yards.
29mins: GOAL. Superb volleyed pass from Ziege found Keane away from last defender, through on Hoult and finished in style. 2-0.
31mins: YELLOW. Ziege for foul on Roberts.
41mins: Koumas run and shot over from 20 yards.
43mins: CHANCE. Keane beat offside trap, clear on goal, tried to slide ball past Hoult who stayed big and deflected the ball over.
Half-time: Spurs 2-0 WBA
47mins: Carr low cross deflected off a defender away from Keane.
54mins: Deep cross from Ziege to Carr, cross met by Keane but effort blocked by Wallwork.
55mins: SUB. Dobie for Hughes.
60mins: Keane break down the right, low cross aiming for Davies at far post clipped Gregan's foot and went straight to Hoult.
63mins: SUB. Iversen for King.
66mins: YELLOW. Koumas onto long ball over the top, Keller out of his box to meet him, brought down, no red card. Keller then saved resulting free-kick from Koumas.
72mins: GOAL. McInnes broke through a few challenges, ball fell to Dobie, struck into into corner across Keller from 25 yards. 2-1.
74mins: SUB. Poyet for Sheringham.
75mins: YELLOW. Clement for foul on Carr.
77mins: CHANCE. Clement headed Koumas' corner wide from seven yards.
78mins: Superb defending from Sigurdsson to head clear of Iversen right under crossbar from Carr's cross.
80mins: GOAL. Richards flicked on Davies throw, Iversen onto loose ball, shot saved by Hoult but Poyet stabbed loose ball home. 3-1.
81mins: SUB. Dichio for Roberts.
83mins: Carr hounded Gregan into mistake, Keane attempted chip over Hoult went into stand.
84mins: SUB. Adam Chambers for Johnson.
Line-ups: Spurs: Keller, Carr, Ziege, Perry, Richards, King (Iversen, 63), Davies, Anderton, Redknapp, Sheringham (Poyet, 74), Keane. Subs: Hirschfeld, Ferdinand, Doherty.
West Brom: Hoult, Balis, Clement, McInnes, Wallwork, Johnson (A Chambers, 84), Roberts (Dichio, 81), Gregan, Sigurdsson, Koumas, Hughes (Dobie, 55). Subs: J Chambers, Murphy.
Attendance: 35, 958.
Goals from Christian Ziege, Robbie Keane and Gus Poyet steered Spurs to a comfortable looking 3-1 win over West Brom - but the team did not have it all their own way against the spirited Baggies.