Arsenal manager Arsene Wenger said: "When we were 1-0 up with a few minutes left, I thought of the final against Liverpool in 2001.
"We didn't score the second goal and they caught us with two goals in the last few minutes. We needed to score the second goal today and Robin did that with great style."
Arsenal had to work hard to gain the ascendancy against well-organised opponents, whose physical approach upset them for most of the first half. Garry Flitcroft, David Thompson and Aaron Mokoena were all booked for fouls.
Mark Hughes has made Blackburn a hard team to break down. But once Pires had shot Arsenal into a 42nd-minute lead, his side were always struggling. They lacked the attacking threat to trouble the Gunners.
Wenger was unhappy with Blackburn's first-half tactics. He said: "They tried to stop us playing. The referee took charge of the game only slowly. We responded with great dignity to some over-the-edge challenges."
Midfielder Gilberto added: "They tried to provoke us but we kept our concentration. They marked us very tight."
Hughes said: "For long periods, we did a good professional job. I thought we were the better side until we conceded just before the break.
"Arsenal should just be glad they've got through a difficult game rather than talking about my players."
Arsenal skipper Vieira summed up: "We expected a tight game and a physical approach.
"Blackburn started well, but we responded very well. We kept calm and kept playing the ball on the ground. We controlled the game after the first goal. Then Robin came on and settled it at the end. I think it was a fair result."
Arsenal achieved the win without the Premiership's top scorer Thierry Henry, out with a groin inflammation, and England centre-back Sol Campbell. Both should be fit for the final.
Blackburn began with a packed midfield and Paul Dickov as a lone striker. Mokoena sat in front of their defence.
They tried to snap at Arsenal's heels from the start. Flitcroft's opening challenge on Bergkamp was a taste of things to come.
Yet Rovers came close to grabbing a sixth-minute lead. Dickov ran onto a long ball and lobbed over Jens Lehmann into the net. A marginal offside decision reprieved Arsenal and Blackburn rarely threatened again.
The Gunners dominated possession but lacked penetration early on. It was 29 minutes before they troubled Friedel when Jose Antonio Reyes fired in a low shot after a break by Vieira.
Bergkamp worked the first real opening in the 37th minute, a delightful flick that set up Reyes. Friedel made a brilliant diving save, then Morten Gamst Pedersen blocked Pires' follow-up. That move seemed to galvanise Arsenal.
Dickov, who began his career with Arsenal, had forecast: "If the lads at the back can build a platform, we've got a chance." Suddenly they were stretched.
Three minutes before the interval, Kolo Toure arrived unmarked at the far post to collect Vieira's diagonal cross. The defender calmly checked back and picked out Pires who stroked in from five yards.
Blackburn began the second half with a more attacking approach. Hughes sent on Brett Emerton and switched to 4-4-2 with Pedersen up alongside Dickov. Now the game became more open.
Friedel made a fine 52nd-minute save to beat away Gilberto's close-range shot. Substitute Cesc Fabregas had a shot blocked by Dominic Matteo before Arsenal swept the ball around in a confident 45-pass movement. Their fans loved it but their team still needed a second goal to kill the tie.
Emerton emphasised that when he cut in from the left and forced Lehmann to make a diving save.
Arsenal seemed content to play on the break. Hughes sent on Robbie Savage to freshen up Rovers' midfield. Savage has hardly played for six weeks because of groin trouble but he made little impact.
With time running out, Hughes played his last card, introducing striker Jon Stead and gambling on three at the back.
Van Persie caught them out four minutes from time. The Dutchman spun on Vieira's pass, nipped past two challenges and passed his shot beyond Friedel.
Another decisive finish four minutes later finished the contest. Blackburn defender Andy Todd seemed to elbow the Dutchman after he shot but Van Persie's joy at the final whistle was unrestrained.
Hughes said ruefully: "We had to chase the game and they had the quality to punish us in the last ten minutes."
Steven Reid headed Blackburn's best chance tamely at Lehmann a minute after Van Persie's first goal. They simply lacked the firepower to break down the Gunners.
Hughes has revived Blackburn and saved them from relegation. A striker will be his top summer target as he aims to continue their improvement.
So Arsenal go on to try and lift the FA Cup for the tenth time in their history. Blackburn have not reached the FA Cup final since 1960 - and their last FA Cup final victory came in 1928.
MAN OF THE MATCH: Robert Pires (Arsenal) – Scored the vital opening goal that eventually ended Blackburn's stubborn resistance. The Frenchman was a key figure in Arsenal's winning display, continually probing and expertly linking up play.