Goals from Darren Dods, Christian Kalvenes, Craig Conway and Morgaro Gomis cancelled out Andrew Consodine's opener for Aberdeen and saw Craig Levein's men fire their way to Hampden.
Cheered on by the noisy Tangerine Army, United started the game brightly. With just seven minutes on the clock, a cross from Kalvenes on the left found Mark de Vries and his knock-down fell into the path of the on-rushing Robertson, but Barry Nicholson managed to clear.
United then had the first attempt on goal on 12 minutes when Noel Hunt latched on to a de Vries flick on but his shot flew wide.
Then against the run of play, Aberdeen took the lead on 18 minutes. A corner from the right by Barry Nicholson was headed goalwards by Zander Diamond but United failed to clear the danger and Consodine slammed home from close range.
United hit back almost immediately when on 22 minutes Kalvenes whipped in a free-kick from the right and Darren Dods headed home from six yards.
After 38 minutes, United won their first corner and almost went in front when Conway's cross was met by Dods, whose glancing header went just wide with Lee Wilkie stretching but unable to make a vital touch.
United went into the break at 1-1 but were the dominant team.
In the second half, with the Arabs behind Jamie Langfield's goal, the former Dundee keeper was clearly unsettled by the hostile reception and when he scuffed a simple pass-back, United seized the opportunity.
The resulting corner from Conway was met full-on by Kalvenes and his bullet header put the Tangerines back in front on the hour mark - sending the supporters into raptures.
On 65 minutes, United went 3-1 up when Conway latched on to a long ball and the advancing Langfield slipped to leave an open goal, and the United winger had the simple task of slotting slot the ball into the empty net.
Two minutes later, the United fans had further reason to cheer when a moment of madness from Lee Miller led to his second bookable offence. A late lunge on Kalvenes gave the referee no option but give him his marching orders.
United went on to seal their place in the Hampden showdown with Rangers when a short back-pass from Severin was charged down by Morgaro Gomis, who rolled the ball over the line to put his side 4-1 in front and leave the Arabs screaming for more.
Teams:Aberdeen: Langfield; Consodine, (Aluko, 66); Foster; MaNamara, (Bus, 77); Diamond; Severin; Walker; Nicholson; Young; Mackie; Miller; (Subs: Maguire; Maybury; Soutar)
Dundee United: Zaluska; Kalvenes; Wilkie; Dods; Flood, (Dillon, 77) ; Kerr; Robertson; Conway; Gomis, (Buaben, 77); Hunt; De Vries; (Subs: Kenneth; Odhiambo; McLean)
Pic courtesy of Mark Davison.Click
here for the full report by Baktosch Gillan.