The Irish star gave a master class in lethal marksmanship to bag a hat-trick and secure the points against a determined Everton outfit that just wouldn't go away.
After initially trailing in the first half we led 2-1 and 3-2 only for the vistors to level on each occasion.
But Keane's hat-trick goal, all his own work after Alan Stubbs misjudged Gary Doherty's header, finally wrapped up the points seven minutes from time.
It was quite a show - no lack of team spirit here - and just what the doctor ordered after last week's FA Cup exit.
The first half lacked any real pattern as both sides tried to take control.
Everton, with ex-Spur Espen Baardsen a last-minute replacement in goal for the injured Richard Wright, took an early lead with the first real attack of the game as debutant McBride raced onto Gemmill's fine pass, had just enough pace to hold off Doherty and calmly slid the ball past American team-mate Kasey Keller.
To the lads credit, we hit back straight away. Anderton's corner was cleared to the 18-yard line where Davies won a crucial header back into the danger zone and Poyet flicked his header home from 12 yards.
Everton remained a threat and Watson crept between defenders to force a fine save from Keller after 17 minutes. Radzinski, whose pace caught the eye, then shot over from 20 yards.
Anderton and Poyet lashed in shots from distance and Anderton's teasing free-kick from the left somehow missed everyone including Iversen creeping in at the far post.
The final action saw Carr's 30-yarder force a scrambling save from Baardsen to his left.
The second half was a different story with goal action aplenty in a real ding-dong affair.
It took only four minutes for us to take the lead for the first time as Anderton's pass split the Everton defence, Keane took the ball comfortably in his stride before dragging it past Baardsen and tucking it away.
Baardsen saved superly from Davies minute later but Keller had to be at his best to deny Stubbs as Everton hit back. From the corner that followed Keller's save, Iversen fluffed his clearance and Watson smashed home from close range for 2-2.
Poyet and Keane went close but it was Keane who struck again after 67 minutes. This time he slipped away from Yobo to receive Anderton's pass and in a flash, fizzed a low drive into the bottom corner from 25 yards. It looked like everything he touched would turn to gold.
Iversen had a tricky chance to make it 4-2 from the pass of the game from Davies but, incredibly, it was the visitors who scored next to level again. This time Li Tie hit Watson, he diverted the ball to Radzinski and the Canadian made no mistake from 12 yards. Sixteen minutes left, 3-3.
There could be no doubt as to where the hero would come from though.
With seven minutes left, Stubbs got underneath Doherty's clearance, Keane snapped it up, ran towards goal, slipped Yobo and dinked over Baardsen.
It was the first hat-trick since Les Ferdinand's against Bolton in the Worthington Cup last season and worth the admission alone.
10mins: GOAL. First dangerous attack at either end, McBride onto Gemmill's through ball, held off Doherty to calmly place ball past Keller. 0-1.
13mins: GOAL. Corner half-cleared and Poyet latched onto loose ball, heading beyond Baardsen into the corner from 12 yards. 1-1.
17mins: SAVE. Keller down well to his left to palm away Watson's header.
25mins: Decent Everton move ended with sharp turn and shot over from Radzinski.
27mins: Anderton stinger from 30 yards dealt with by Baardsen.
28mins: YELLOW. Gemmill for foul on Bunjevcevic.
32mins: CHANCE. Teasing free-kick from Anderton missed everyone including Iversen, just two yards out at the far post.
33mins: Poyet flashed difficult chance over from 20 yards after chest down from Iversen.
37mins: Stubbs piledriver from 25 yards whistled over.
42mins: Carr 30-yarder left Baardsen scrambling to save to his left.
Half-time: Spurs 1-1 Everton
48mins: Pistone drive comfortable for Keller.
49mins: GOAL. Brilliant pass from Anderton split Everton's defence, superb control from Keane who then dragged it past Baardsen and finished in style. 2-1.
51mins: SAVE. One-two between Carr and Poyet, deep cross fell to Davies, 10 yards out, magnificent save from Baardsen low to his right.
57mins: SAVE. Keller reaction block to deny Stubbs header from Li Tie's deep cross.
57mins: GOAL. From corner, Iversen made hash of clearance and Watson lashed home from close range. 2-2.
61mins: Flying header from Poyet straight at Baardsen.
66mins: Keane curler from edge of the box just wide.
67mins: GOAL. Another superb effort from Keane. Managed to slip Yobo to receive Anderton's pass and fired low into the corner in a flash from 25 yards. 3-2.
71mins: CHANCE. Volleyed pass from Davies released Iversen, ball always tricky, attempted lob just wide.
74mins: GOAL. Watson diverted Li Tie's pass into path of Radzinski who made no mistake from 12 yards. 3-3.
76mins: YELLOW. Doherty for foul on Gemmill.
79mins: Anderton free-kick flew just wide.
79mins: SUB. Acimovic for Iversen.
83mins: GOAL. Keane hat-trick. Stubbs misjusdged Doherty's header forward, Keane latched onto it 40 yards out, slipped past Yobo and dinked ball over Baardsen. 4-3.
86mins: SUB. Carsley for Yobo.
90mins: SUB. Osman for Li Tie.
Line-ups: Spurs: Keller, Carr, Bunjevcevic, Perry, Anderton, Doherty, Poyet, Iversen (Acimovic, 80), Keane, King, Davies. Subs: Sullivan, Taricco, Blondel, Gardner.
Everton: Baardsen, Watson, Pistone, Stubbs, Unsworth, Radzinski, Li Tie (Osman, 90), Naysmith, Gemmill, McBride, Yobo (Carsley, 86). Subs: Alexandersson, Pembridge, Said.
Robbie Keane's super show secured the vital three points as we kick-started our bid for Europe via the Premiership in a thriller.