Cristiano Ronaldo was unable to repeat the feat of scoring within two minutes of kick-off achieved in his last two games and the first chance of the match fell to the visitors on 15 minutes.
A neat one-two resulted in Martinez dragging his low left-footed shot wide of the far post.
The first-half display of Real Madrid was far from impressive and the side lacked the creativity that has been supplied in abundance by Kaka in recent weeks.
In one moment of note from the first 45 minutes, a dangerous studs-up lunge by Dutch left back Roysten Drenthe on Marc Bertran resulted in a fractured tibia for the Tenerife defender.
Raul failed to convert RealÃ¢â‚¬â„¢s best opportunity after 28 minutes.
A drilled Ronaldo effort deflected into the SpaniardÃ¢â‚¬â„¢s path and his left-foot volley was struck straight at the body of goalkeeper Aragoneses from point-blank range.
Real could only muster fleeting attacks, predominantly involving Benzema and Ronaldo in the channels, but both failed to provide a final ball of any quality.
Tenerife Ã¢â‚¬â€œ who racked up four yellow cards within 35 minutes Ã¢â‚¬â€œ shaded the possession in the first half and the home fans demanded better from their side after the break.
Pellegrini made the kind of tactical decision associated with Jose Mourinho at half-time Ã¢â‚¬â€œ bringing on both Kaka and the in-form Guti for Sergio Ramos and Granero.
Lassana Diara was deployed at right full-back and the Chilean coachÃ¢â‚¬â„¢s decisions paid off immediately.
Karim Benzema scored the opener with a superb downward header from Xabi AlonsoÃ¢â‚¬â„¢s cross on 47 minutes.
Tenerife reacted well and tested Casillas from long-range via RomanÃ¢â‚¬â„¢s curling effort, and Real had to scramble the ball away from the resulting corner after it was header back into the melee of players.
Ronaldo almost bagged another sensational solo goal for the season on 56 minutes.
The superstar burst forward with the ball at his feet in his own half and drove towards goal, racing past two defenders in the box, only to be denied by AragonesesÃ¢â‚¬â„¢ brilliant tip over the bar.
Ronaldo rose highest from the resulting corner, but failed to keep his header down from 10 yards out.
Two minutes later, Benzema grabbed his and RealÃ¢â‚¬â„¢s second of the game and highlighted the gulf in class between the two sides.
A lofty clearance by Drenthe from the back eluded Manolo and was raced onto by the young Frenchman who out-muscled the defender and placed a right-footed shot past the despairing Tenerife goalkeeper with aplomb.
The summer-signing almost bagged a hat-trick just past the hour mark.
Kaka played a ball for Benzema to shift and shoot agonisingly wide of the far post with his left-foot.
Moments later, the striker found Ronaldo in acres of space with a measured cross and the Portuguese international failed to continue his record-breaking goal-scoring run with a shot that was palmed away by Arogenses seven yards from goal.
Casillas made amends for several unconvincing moments in the Real goal by pulling off a superb double-save on 75 minutes.
Daniel Kome beat Drenthe and darted into the box before squaring the ball for Alfaro to see his low shot that looked destined for the bottom corner saved by Casillas. The Spanish goalkeeper then dived in bravely to block NinoÃ¢â‚¬â„¢s follow-up for which a free-kick was to be awarded in the home sideÃ¢â‚¬â„¢s favour.
Kaka put the result beyond doubt with a sublime third for Real on 77 minutes.
The ball fell kindly for the Brazilian following an effort on goal by Raul and he proceeded to power a superbly-executed curling strike into the top corner to send Real a goal clear at the summit of the La Liga table.
Real Madrid: Casillas, Sergio Ramos (Guti, 45), Pepe, Albiol, Drenthe, Lass, Alonso, Granero (Kaka, 45), Raul, Benzema, Ronaldo (Diarra, 80)
Tenerife: Arogeneses, Bertran (Sicilia, 37), Manolo (Omar, 62), Llorens, Roman, Luna, Alonso, Nino, Alfaro, Richi, Kome (Dinei, 81)
Man of the Match: Kaka Ã¢â‚¬â€œ Completely transformed the style of RealÃ¢â‚¬â„¢s play after his half-time introduction and scored a beautiful goal to send them top.
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