By Alex Livie
Last Updated: 01/01/70 1:00am
Gary Doherty had given Spurs the lead against the run of play on 13 minutes, showing remarkable instincts to glance the ball home, but The Gunners continued to hoard play and were rewarded when Vieira headed home the equaliser shortly after the half-hour.
Despite missing a glut of chances, Arsenal eventually found a way past Neil Sullivan on 73 minutes when Vieira won the ball in midfield and beat three players before sending Sylvain Wiltord away down the right.
The striker crossed superbly and Robert Pires had the simple task of rolling the ball into an empty net.
It was just reward, as Wiltord, Henry, Pires and others missed chances to kill the game before the French axis combined to sink Tottenham.
Man of the Match Patrick Vieira spoke after the game, saying: "We showed our experience of the big game and I think we deserved to win the game.
"It was worrying to miss so many chances in a major game, as you do not always get so many chances, but we eventually scored and we deserved the win."
Arsenal were the only team in the game in the opening exchanges, with Vieira controlling play from the midfield. He fed Pires, who rolled the ball into the path of Wiltord, but his shot fizzed high and wide.
The Gunners had a lot of success down the right throughout the match, with Lee Dixon a constant menace. However, as was often the case, the final ball was wasted with the full back only finding Spurs keeper Neil Sullivan with his cross when there were men free in the box.
Spurs were camped in their own half for long periods but they made their first attack count, with Doherty showing great instincts to score.
The defender created the chance himself, causing havoc in the box. The ball fell to Les Ferdinand, whose shot was well saved by David Seaman, but Dixon failed to clear his lines and Doherty took advantage of Stefan Iversen`s wild shot to glance the ball home.
Pires had a chance to level moments later, but he appeared reluctant to shift the ball onto his left and shot tamely at Sullivan with his right.
The right-hand side was the source of Arsenal`s leveller, as Sol Campbell cynically obstructed Parlour as he galloped clear and referee Graham Poll awarded a free-kick.
As Campbell was off the field receiving treatment, Vieira capitalised on the England man`s aerial absence, rising majestically to head a Pires centre past Sullivan.
Tottenham`s woes were extenuated when Campbell suffered an ankle injury in fouling Parlour and had to be substituted.
An area of play that is sure to be a source of concern to Gunners boss Arsene Wenger is his side`s failure to kill teams off, and the final ball was again lacking as Parlour raced clear, again down the right, but he shot wastefully wide when the unmarked Wiltord was pleading for a pass.
A rare Tottenham foray saw Sergei Rebrov shoot wide, but the red tide again flooded forward, but Wiltord failed to capitalise on some incisive Henry play as he dallied and was crowded out by a mass of Spurs defenders.
The pattern of play continued after the break, with Silvinho, always one for a spectacular shot, firing a dipping effort narrowly over the bar.
Sullivan, who has been a hero for Spurs on their cup run, produced a fine save to deny Henry. The Scot dived at the feet of the Frenchman and diverted the ball to safety.
Shortly before the hour, Wiltord again found himself beyond the defence, but he delayed his effort and Sullivan was able to make a superb save.
Pressure eventually told, as Vieira, the orchestrator of Arsenal`s attacking play, won the ball and strode through Spurs defenders before feeding Wiltord, who eventually produced a fine cross for Pires to gleefully poke the ball home.
Spurs tried to respond, with Rebrov firing a volley straight at an underworked Seaman, but the reliable Gunners back-line held firm to secure Wenger`s boys` trip to the Millennium Stadium for the FA Cup final.
A delighted Wenger said: "I believe that we won the hard way, as we created chance after chance and were 1-0 down after 20 minutes.
"Unfortunately we missed chances and, in football, you wonder if you will be made to pay but we did enough to win."
Speaking about Vieira, Wenger said: "He is phenomenal."Patrick had a wonderful game. Even when he is tired he is a player who finds the reserves to be decisive.
"I don't think there is a better player in that position and I feel he deserves to be Footballer of the Year."