Goalkeeper Neil Stacey proved the hero, saving a spot-kick from Martin Hutchcox to atone for a mistake in normal time which had allowed United to pull level.
United were rocked in the opening stages when goalkeeper Joe Connor was forced off with a stress fracture of his tibia following a 50-50 challenge with Whitnash striker Ross Briscoe.
He was replaced by centre-half Hutchcox, who was beaten soon after by a Charlie Smith shot, only for the ball to hit the outside of the post and run dead.
Whitnash made the breakthrough in the 37th minute when Luke Cole raced on to a Briscoe flick-on and neatly slotted past the onrushing Hutchcox.
United’s task was made even harder shortly before the break when they had a player sent off for something he said to the assistant referee.
However, rather than sit back, the ten men pressed Town back and held the upper hand for the opening 20 minutes of the second period.
They got their reward when a Josh O’Grady free-kick from 25 yards out squirmed out of the hands of Stacey and into the net.
Whitnash responded well but a combination of good goalkeeping and poor finishing denied Briscoe, Cole and Lewis Currell and meant the tie had to be decided on penalties.
Clinical finishing from Town ensured they scored all five of their kicks, with Stacey’s save enabling them to go through 5-3.
“We were great in this game and our character and quality was clear for all to see,” said manager Barry Shearsby.
“We are delighted to have beaten a very good Cov United side and progressed into the final - every player showed me just what they are made of and were superb.”