Arsenal, who drew 2-2 in last week's semi-final, first leg, completed a 5-3 aggregate win after Aliadiere struck on the stroke of halftime in extra time and a Tomas Rosicky shot found its way in off Spurs defender Pascal Chimbonda.
Togo striker Emmanuel Adebayor looked to have won the north London derby for Arsenal with a 77th-minute strike, only for Egypt striker Mido to head Spurs an 85th-minute equaliser just five minutes after coming off the bench.
Arsenal will meet the Premier League champions for an all-London final at Cardiff's Millennium Stadium on February 25.
"When Spurs came back to 1-1 of course we needed to be mentally strong," A¦rsenal manager Arsene Wenger said.
"We were wobbling a little bit for a few minutes, then in extra time it was all us," he told Sky Sports.
"The experience of (substitute midfielder Cesc) Fabregas was the key, he gave us more security to keep the ball."
The hosts, starting out with another largely second-string side for this competition, were rewarded for an attacking performance at the Emirates Stadium that kept Spurs under pressure for long periods.
Both sides squandered golden early chances, with Spurs striker Robbie Keane put clean through by a long ball but failing to beat the outrushing keeper Manuel Almunia.
Arsenal defender Kolo Toure fluffed an easy follow-up two minutes later after Spurs' England keeper Paul Robinson could only parry a shot from busy 18-year-old Brazilian midfielder Denilson.
Despite the pressure, Spurs defended with real grit and might have snatched the lead when French midfielder Steed Malbranque rose to meet Hossam Ghaly's cross from the right with a powerful header that flew just wide.
HIGH TEMPO
There was no let-up in the tempo after the re-start, with Arsenal dominating but teenage winger Theo Walcott failing to make the most of his pace and being replaced on 65 minutes by Czech midfielder Tomas Rosicky.
Adebayor broke the deadlock in the 77th minute in the wake of a fine snap shot by Rosicky. Arsenal returned to the attack, Rosicky picked up possession and dinked the ball through for Adebayor to run in and steer past Robinson.
Spurs levelled when Denilson conceded a free kick, England midfielder Jermaine Jenas curled the ball over and Mido rose highest to send a glancing header past a stranded Almunia.
Mido nearly settled it minutes later with a shot from the edge of the area which just missed the left-hand post, but the tie soon headed into extra time.
Spurs had finished strongly but extra time was more balanced and swung Arsenal's way in the 105th minute.
Spurs substitute defender Ricardo Rocha tried to clear with a diving header, the ball ran for Aliadiere and the Frenchman drilled a low shot past Robinson.
Arsenal finished the job when Rosicky's turn and shot hit the woodwork and the luckless Chimbonda knocked the ball over the line as he tried to clear.
Victory sealed the hosts' trip to Cardiff and extended an unbeaten record against Spurs in all competitions since 1999 to 17 games.
