Keane himself was felled just after the half-hour and did the honours to shoot us into a lead that really should have been increased in what was almost certainly our most impressive performance on the road this season.
It made it a perfect beginning to the Easter programme with Manchester United set to arrive at the Lane on Monday.
It was a full-house at Goodison on a sunny spring-summer type of afternoon, with the Tottenham travelling army in fine voice on the Bullens Road side of the ground.
Mido was missing from the squad with a groin injury, which led to a recall to the starting XI for Jermain Defoe - along with a chance on the bench for 20-goal reserve team striker Lee Barnard.
It meant Defoe at the spearhead of our attack with Keane in a slightly withdrawn role. After our experience up at Newcastle, you got the sense that getting through the first 15 minutes or so unscathed would have a big bearing on our afternoon's fortunes. As it turned out, the boys were pinging the ball around with a fair degree of confidence and there were a few early groans from the home support.
Lee Carsley was first in referee Mr Webb's book just before the ten-minute mark for a fierce lunge on Anthony Gardner. Nine minutes later we came the closest to making an opening when Michael Carrick presented a crossing opportunity to Aaron Lennon. The flight of the ball beat Richard Wright in the Everton goal, but asked too much of Gardner to head at the far post. A low Keane drive moments later did not really test Wright.
Another devilish Lennon cross came so close to unlocking the gate, Teemu Tainio's connection being blocked by the midrift of Wright at the near post - although it was clear the keeper knew little about it.
The scoring was opened on 32 minutes after a dash down the left by Lee Young-Pyo. The Korean squared the ball across the edge of the area and was picked up by Keane, who strode forward to strike before being bundled over by Alan Stubbs. Mr Webb showed no hesitation in pointing to the spot - although Jenas did forced the loose ball into the net - and Robbie was similarly decisive with his kick, which gave Wright no chance down to his left.
Gardner was then the victim of another awful challenge - this time by Philip Neville - but was also cautioned himself for his reaction to the incident. A header back across goal from the defender offered Jenas the opportunity for a nod goalwards, but his effort cleared the crossbar with Everton rocking.
There was a change after the break with Danny Murphy replacing Tainio, who took a knock before the interval. For Murphy it was a return to Merseyside against a team he scored a winner against at this venue during his time with Liverpool.
Tim Cahill had the chance to level after an unkind bounce off of Ledley King, with the skipper brilliantly retrieving the situation. Defoe then picked out the run of Jenas at the other end and Wright reacted well to his shot on the run, but it should have been a goal.
He reacted even better seconds later when Gary Naysmith made a hash of steering the ball back to the keeper, the ball landing at the feet of Defoe in front of goal and the latest of touches from Wright diverted his shot just wide of the post.
On 54 minutes it really should have been two when Defoe caught the home side up field and sprinted away on the break. He went on to pick out the run of Murphy who, in turn, located Keane inside the area to the left. Robbie left his man standing to work space for a shot, but went for the top corner and misfired.
Lennon then created further mayhem but opted to pass inside the area when a shot was on, before Jenas completely out-paced Stubbs but support was not quick in coming and Everton recovered. James Beattie did have the ball in our net just before the hour but the flag went up early - and correctly.
Keane could have scored again when Lee again spotted him advancing towards the area, the striker opting for precision rather than power - for which Wright was probably very grateful. Without bias, Everton shouldn't have still been in the game and the response was the introduction of Duncan Ferguson.
The boys went on to indulge in some time-consuming keep ball which ended with the ball finding Defoe on the edge of the area and a whipped in shot which rattled the underside of the bar.
Calum Davenport was next off the bench on 82 minutes for just only second first team appearance, his debut coming up front against Aston Villa away last term. It was Lennon who departed, with Davenport forming an extra layer in the centre of defence.
With the added protection it was a case of seeing it out - and see it out the boys did.
Robbie Keane netted his 15th goal of the season from the penalty spot as we recorded a sixth away win of the season and a Premiership double over Everton.