A Dean Windass double was not enough for Hull after a virtuoso performance from Hungarian midfielder Peter Halmosi gave Plymouth a dramatic victory at Home Park.
Halmosi was at the heart of everything for the home side and his two first-half free-kicks caused turmoil in the Hull defence as Nadjim Abdou gave the Pilgrims the lead before another tantalising set-piece from the Hungarian midfielder made it 2-0 at half-time.
Second-half substitute Windass struck twice either side of a Sylvan Ebanks-Blake goal in a frantic 10 minutes to give the determined visitors hope, but it was not to be as the Pilgrims progressed to the fourth round.
It was the home team who started the brightest as thunderous shots from Ebanks-Blake and Halmosi forced Boaz Myhill to make two great saves at full stretch within the first 20 minutes.
The Pilgrims continued to press and did not have to wait long before their dominance was converted into goals.
After Tigers defender Sam Collins had hauled down Ebanks-Blake on the right, Halmosi's free-kick was met by French midfielder Abdou, who slotted home from the centre of the penalty area in the 21st minute.
Just three minutes later the home side had doubled their lead when Halmosi's set-piece delivery again caused havoc as the visitors' defence failed to cope with his 35-yard free-kick and the ball evaded everyone before creeping into the net.
But Hull finally found their feet a minute before the interval when Stuart Elliott's shot was blocked before falling to Nick Barmby who fired in a ferocious effort which goalkeeper Luke McCormick saved brilliantly.
Tigers boss Brown sent on fans' favourites Windass and Richard Garcia after the break and the change had an immediate effect as the visitors' confidence seemed to improve dramatically.
And they were soon back in the match as the seemingly ageless Windass struck in the 51st minute to give the visitors hope.
The 38-year-old defied his years to latch onto Barmby's knock-down before exquisitely lobbing the advancing goalkeeper to make it 2-1.
All of a sudden the game came to life and both sides had their chances in a furious period of football.
Garcia almost levelled for the Tigers with a fantastic header three minutes after Windass' strike but it was the Pilgrims who found the back of the net as Ebanks-Blake scored his 13th goal of the season.
Halmosi was pivotal again as he went on a mazy run before laying the ball unselfishly to the former Manchester United man who made no mistake with his curling effort from the edge of the box to make it 3-1 in the 57th minute.
But just as Plymouth began to breathe easily once again, Windass was on hand in the 59th minute to set up a grandstand finish to a pulsating FA Cup tie.
Referee Paul Taylor awarded a free-kick to Hull after defender Marcel Seip was adjudged to have fouled £1million man Caleb Folan and Windass stepped up to curl the 25-yard free-kick past a sprawling McCormick to reduce the deficit to just one goal again.
Manager Paul Sturrock refused to let his side sit on their one-goal lead and urged them forward.
His tactics would have paid dividends but Hull keeper Myhill pulled off a string of fine saves to deny Luke Summerfield and then Halmosi as the home side sealed their progression through to the next round.
Teams:
Plymouth McCormick, Connolly, Doumbe, Seip, Hodges (Sawyer 61), Summerfield (Chadwick 90), Abdou, Nalis,Halmosi, Easter, Ebanks-Blake (Jutkiewicz 85).
Subs Not Used: Larrieu, Fallon.
Booked: Easter.
Goals: Abdou 23, Halmosi 26, Ebanks-Blake 58.
Hull Myhill, Doyle (Atkinson 77), Turner, Collins, Delaney,France, Marney, Livermore (Garcia 46), Elliott (Windass 46), Folan, Barmby.
Subs Not Used: Dawson, Featherstone.
Booked: Marney.
Goals: Windass 51, 60.
Att: 12,419
Ref: Paul Taylor (Hertfordshire).