Keane struck almost identical goals either side of the break before a delightful finish from Defoe put the issue beyond doubt after 57 minutes.
In doing so, Keane helped exorcise the ghosts of our last visit to Turf Moor in November 2002 when we lost 2-1 to the Clarets in the same competition - he and Simon Davies were the only survivors of that night to play this time around.
The scoreline doesn't tell the full story though. Burnley, themselves hit by injury, created the better chances in the first half and might well argue that they should have been ahead by the time Keane opened the scoring.
They had further chances before the break as well but once Keane buried the second, it was, in reality, all over.
Jol made changes for his first game in charge. Michael Carrick came in for his first start for the club, Stephen Kelly made his first start this season, Reto Ziegler replaced Simon Davies and Michael Brown returned to central midfield.
Robbie Blake, starting up front on his own, was Burnley's talisman again and created an early chance for Richard Duffy before shooting just wide himself.
Noe Pamarot twice went close from Ziegler set-pieces before Blake crossed again for Duffy who climbed above Kelly but failed to connect with a good headed chance after 29 minutes.
The home side were made to pay two minutes later as we opened the scoring.
It was a fine goal as well as Pedro Mendes released Carrick down the right flank and his perfectly-angled low cross was buried by Keane at the far post.
Burnley hit back to carve out another two chances before the break.
The first was the best after 43 minutes as Tony Grant met Mohamed Camara's cross only for Paul Robinson to tip away at full length. The keeper had to be alert when Michael Duff's met Blake's ensuing corner with a powerful header and Blake was in the thick of it again seconds before the whistle, firing wide from a decent position.
The second half was a different story as we wrapped up the tie with two goals in six minutes.
The second goal after 51 minutes was similar the opener with Defoe and Ziegler combining down the left flank before Defoe delivered a wonderful cross with the outside of his right foot to allow his strike partner to tap home from close range.
Defoe's goal bettered that, however. Keane was involved again, this time flicking Kelly's pass around the corner for Defoe, who worked a yard, spotted Jensen off his line and curled into the top left corner from 25 yards.
GUIDE TO THE ACTION
18secs: Decent early cross from Blake headed away from danger by Kelly.
5mins: CHANCE. Blake broke offside trap, left channel, picked out Duffy on the edge of the box, sidefoot effort on full volley straight at Robinson.
9mins: CHANCE. Lovely in-swinging free-kick from right touchline by Ziegler met by Pamarot, looked unclear that he had so much space and elected to nod back towards Defoe.
11mins: CLOSE. Free-kick into Blake who spun away from Naybet, left-foot shot across Robinson just wide.
14mins: Clever short passing as Naybet joined in from back, attempted little dink into Keane cleared.
19mins: More possession now, Brown released Mendes down right, cutback to Keane, shot from 20 yards deflected slightly, Jensen gathered comfortably.
22mins: CLOSE. Superb corner from Ziegler, Pamarot there to meet in front of goal, keeper could only spread himself but Pamarot didn't connect properly with header, hit Jensen and out for corner.
24mins: Ziegler skipped past Duffy, strode forward, left side, elected to shoot from 22 yards, straight at Jensen.
25mins: Clever reverse pass from Pamarot into Keane in box, looked to drive across goal where Defoe was lurking, deflected wide.
28mins: Keane laid ball into path of Defoe, 25 yards out, worked a yard but lashed over.
29mins: MISS. Chance of game so far, Blake quick exchange of passes with Sanokho, cross from left found Duffy climbing above Kelly but flicked header wide from 10 yards.
31mins: GOAL. Mendes flicked ball down right flank to Carrick, lovely cross across face of goal found Keane to finish from close range.
Burnley 0, Spurs 1
34mins: Keane played overlapping Kelly into box, combination of Jensen and Roche kept him out. From corner, Pamarot header deflected over.
38mins: Long spell of possession football almost led to Defoe through on goal but offside flag up.
41mins: SUB. Valois for Branch.
43mins: SAVE/CHANCE. Camara cross from left met by Grant, effort slightly deflected, fine save to his right by Robinson to tip away. From corner, Duff towering header Blake's delivery luckily straight at Robinson.
Injury time: Blake onto long ball, away from Naybet, dragged half-chance wide from edge of box.
Half-time: Burnley 0, Spurs 1
51mins: GOAL. Great exchange between Ziegler and Defoe down left flank, Defoe superb cross with outside of foot for Keane to tap home again.
Burnley 0, Spurs 2
57mins: GOAL. Keane flick around corner for Defoe from Kelly's pass, Defoe 25 yards out, spotted Jensen off his line and curled over the keeper into top corner.
Burnley 0, Spurs 3
61mins: SUB. Davies for Mendes.
63mins: Davies onside chasing long ball but Jensen good judgement to come out of box and head clear.
64mins: SUB. Kanoute for Keane.
66mins: SAVE. Ziegler fed Kanoute, right side of box, hit shot well and Jensen parried well.
68mins: Ziegler tame shot from distance straight at Jensen.
74mins: Superb free-kick from Blake into danger area again but Kelly managed to clear.
75mins: Ziegler smashed high and wide with his right foot from 30 yards.
77mins: SUB. Ifil for Pamarot.
78mins: BLOCK. Kelly looked certain to score from Kanoute's cutback but Hyde there to block.
82mins: SUB. Pilkington for Valois.
84mins: Good work from Carrick, played in Defoe, didn't put enough on attempted chip.
85mins: Duffy broke througha couple of challenges but failed to get hold of shot, decent chance from 18 yards straight at Robinson.
88mins: Kanoute shot from 20 yards straight at Jensen.
Full-time: Burnley 0, Spurs 3
Line-ups: Burnley: Jensen, Roche, Camara, Duff, Cahill, Duffy, Sanokho, Hyde, Grant, Branch (Valois, 41; replaced by Pilklington, 82). Subs: O'Neill, Scott, Yates.
Spurs (4-4-2): Robinson; Pamarot (Ifil, 77), Naybet, King, Kelly; Mendes (Davies, 61), Brown, Carrick, Ziegler; Keane (Kanoute, 64), Defoe. Subs: Keller, Redknapp.
Robbie Keane and Jermain Defoe delivered the perfect start for Martin Jol in his first game as Head Coach as we overcame a tricky hurdle at Burnley to move into the quarter-finals of the Carling Cup on Tuesday night.