The Irish star, snapped up from Elland Road in September, was inspired, involved in everything and scored a superb, crucial second goal just before the interval.
Leeds, overrun in midfield, offered little in return and we were in control throughout.
Christian Ziege returned from a calf problem and was finally paired with Steve Carr for the first time in the Premiership.
Goran Bunjevcevic returned to his favoured spot in a back three where Ledley King and Dean Richards towered.
But it was up front where we sparked. Teddy Sheringham, who took some real punishment, was involved in everything and Keane was simply different class. He might have told everyone beforehand he didn't have anything to prove, and he doesn't, but he certainly played that way.
Considering what happened last week, the first half was as good, if not better, than performances against Chelsea, Liverpool, Charlton and, for different reasons, Manchester United.
By contrast, Leeds were poor and their vital statistics in that half were four yellow cards and one shot on target that didn't arrive until the 34th minute.
Keane, causing problems for both Bakke and Wilcox by drifting right, had already been heavily involved early when his presence helped create the crucial opening goal.
Sheringham's pass found the Irish star breaking centrally, he held off Lucic to reach the box before Lucic got a foot in, the loose ball fell to Sheringham who planted a delicious first-time strike with his left foot into the bottom right corner from 20 yards.
For the next 20 minute it was all Spurs with Keane testing Robinson, Kelly back to clear Keane's dangerous cross and Carr sliding in at the far post but unable to keep Bunjevcevic's deep cross on target.
Leeds finally responded with a speculative long-range effort from Kewell forcing a save out of Kasey Keller but play was soon down the other end as Keane left Burns standing before shooting just wide from 30 yards.
It was so one-sided that Terry Venables made a change after just 37 minutes, Viduka on for Burns, but it couldn't stop the inevitable second goal from coming.
It was another corker as well as Poyet picked out Keane's run and the 22-year-old produced a sublime finish into the top corner with the outside of his right foot.
The second half, hardly surprisingly, lacked the sparkle of the first as Leeds went about restoring some pride and we professionally held on to what we had.
Chances were few and far between and outnumbered by yellow cards as the midfield battle became even spikier.
The pick of the chances came our way. Keane, at his tormenting best, couldn't keep a tricky volley down and the pick of the half, somehow swivelled with the ball between his legs on the ground before spinning away from Woodgate and Lucic and cutting the ball back across goal where Sheringham was inches away.
At the other end, Ziege deflected Wilcox's cross straight at Keller and the keeper was out sharply to sweep the ball away from Bowyer after a late break.
MINUTE-BY-MINUTE GUIDE TO THE ACTION
2mins: Bowyer run across the box but dragged shot wide from 20 yards.
4mins: Trickery from Keane took him away from Bakke, right side of area, cut back to Carr who sliced wide.
11mins: GOAL. Quick break from Carr throw, Sheringham's pass found Keane racing clear, held up by Lucic but loose ball fell to Sheringham who planted a delightful left-foot curler into the bottom right corner from 20 yards. 1-0.
14mins: YELLOW. Bakke for foul on Sheringham.
17mins: YELLOW. Wilcox for foul on Poyet.
22mins: One-two between Keane and Sheringham, Keane through, right side of area, fierce shot straight at Robinson.
24mins: Superb work from Keane down right, Kelly back well to avert danger from cross.
29mins: CHANCE. Good possession ended in deep Bunjevcevic cross picking out Carr'a late run around the back of McPhail, slid difficult effort across goal.
30mins: YELLOW. Poyet.
33mins: Lovely move as Anderton spread play to Keane, first-time cushioned volley into Poyet, Bakke did just enough to avert danger.
34mins: First telling contribution from Leeds as Kewell's speculative effort from 30 yards forced Keller into comfortable save.
35mins: YELLOW. Burns for foul on Sheringham.
36mins: Keane trickery left Burns standing, opted for early strike from 25 yards that drifted a couple of yards wide.
37mins: SUB. Viduka for Burns. Switch to Viduka and Smith up front, Kewell wide left.
40mins: YELLOW. Kewell for foul on Freund.
40mins: GOAL. From that free-kick, Sheringham up for header, Poyet onto loose ball and found Keane in a flash, Keane magnificent finish with outside of his right foot into the top corner from 18 yards. 2-0.
45mins: Poyet released Keane, early cross inches away from supporting Sheringham.
Half-time: Spurs 2-0 Leeds United
56mins: Plenty of possession eventually led to Richards chesting down Freund's cross but Keane couldn't get hold of difficult volley.
59mins: Decent cross from Wilcox deflected back towards his own goal by Ziege, thankfully Keller behind it.
65mins: YELLOW. Ziege for foul on Bowyer.
67mins: SUB. Davies for Ziege.
69mins: YELLOW. McPhail for foul on Freund.
72mins: Magnificent skills from Keane held off three defenders, cut ball back into box, inches away from Sheringham.
74mins: YELLOW. Bunjevcevic for foul on Smith.
75mins: Freund nicked ball off Bowyer, squared for Anderton who shot wide from 20 yards.
77mins: SUB. Redknapp for Anderton.
81mins: YELLOW. Smith for foul on Freund.
81mins: SUB. Milner for Viduka.
82mins: Milner spotted Bowyer's break, Keller out quickly to deny him.
85mins: YELLOW. Bowyer for foul on Bunjevcevic.
90mins: SUB. Iversen for Poyet.
Line-ups: Spurs: Keller, Carr, Freund, Bunjevcevic, Anderton (Redknapp, 77), Sheringham, Poyet (Iversen, 90), Keane, Ziege (Davies, 67), King, Richards. Subs: Hirschfeld, Perry.
Leeds United: Robinson, Kelly, Woodgate, Kewell, Bowyer, Burns (Viduka, 38; Subbed for Milner, 81), McPhail, Lucic, Wilcox, Smith, Bakke. Subs: Martyn, Duberry, Richardson.
Robbie Keane ran his former employers ragged as we quickly cast aside last week's disappointments at Highbury to get our European aspirations back on track.