The tie was delicately poised at 1-1 after the first leg but a third minute goal from and an own goal from set Spurs on their way.Robbie Keane, added goals after the break to send Spurs to Wembley where they will play Everton or Chelsea on February 24.The result ended Arsenal's 21 match unbeaten streak against their north London rivals - a run stretching way back to 1999. The game exploded into life when Jenas picked up the ball in midfield and was allowed to run at the Gunners defence before firing a 20-yard shot in-off the far post.
Arsene Wenger traditionally uses the competition to blood his most promising youngsters but playmaker Cesc Fabregas was called into action as early as the 19th minute when Denilson went off injured.
But he was helpless to see Spurs extend their lead eight minutes later when Jenas' swinging free-kick was flicked into his own net by the head of Bendtner with ready to pounce.
And Dimitar Berbatov could have made the game safe shortly after when he went clean through on goal, after Bacary Sagna played him onside, but his shot came off the post and bounced to safety.
Jenas also had an opportunity on the stroke of half-time when he eluded on the left flank and burst into the penalty area only to poke his shot into the side netting.
Arsenal's chances were limited with Bendtner and Abou Diaby shooting narrowly over the top while saved from and tipped Sagna's near post header over the crossbar.
After the break, Keane sealed Spurs' first Cup final appearance since 2002 when a superb pass with the outside of the boot from Lennon sent the Irishman clear and his shot eluded and nestled in the bottom corner.
The Pole should have done better and Arsenal, who beat Spurs at the same stage last season, suffered more frustration seconds later when Bendtner struck the underside of the crossbar with a close-range volley.
Spurs sent their fans into raptures on the hour as a quick counter saw Keane feed Lennon on the right-hand side of the penalty area and he calmly planted the ball between Fabianski's legs.
Wenger called on Emmanuel Adebayor and Eduardo for the final 25 minutes and the Croat fed the Togo striker who unleashed a fierce 20-yard shot into the roof of the net.
But it was far too late to deny Spurs boss Juande Ramos, who has a formidable record in knock-out competitions after winning the UEFA Cup twice with Sevilla as well as the Spanish Cup, from leading his side out at Wembley.
And the icing on the cake came in injury-time when Lennon beat Gilberto on the right flank and crossed for Malbranque to tap home from close range.