Daniel Bentley was again the penalty hero as he saved Alfie Potter's penalty to ensure Blues progressed to the JPT southern-section final against Leyton Orient.
Barry Corr gave Blues the lead early on when he headed home before the home side responded through Tyrone Marsh and then Tom Craddock to lead 2-1 at half-time.
The visitors though came out of the blocks flying in the second-half and were soon ahead. Sean Clohessy levelled things up in the 54th minute before Corr scored his fourth goal in two games to complete the turnaround.
Blues so nearly held on to win it in normal time, but Sean Rigg levelled proceedings with two minutes to go as he headed home from close range.
That sent the game to penalties and after Alfie Potter had his shot saved by Bentley, Elliot Benyon stepped up to send Blues into the southern section final.
Paul Sturrock made two changes, one of those enforced, to the side that drew 2-2 with Brentford on Saturday as Anthony Straker and Chris Barker replaced the cup-tied Marc Laird and Luke Prosser.
Blues couldn't have wished for a better start to the game. With just six minutes on the clock Corr rose highest to head home Kevan Hurst's free-kick for his sixth goal of the season.
But with fifteen minutes gone, the home side were level. Alfie Potter's cross was met by the head of Sean Rigg. He was denied by the reflexes of Paul Smith, but Marsh was on hand to head into an empty net.
That goal had given the home side a lift and they were in the ascendency. Rigg, having been denied the leveller by Smith, then shot just over with a left foot curler.
But Blues' Gavin Tomlin was proving a handful at the other end, and he missed a great chance to put his side back in front when he headed agonisingly wide from Alex Woodyard's cross.
Just after the half-hour mark though and the home side were ahead. Simon Heslop's long ball over the top found Craddock who lobbed the ball over an onrushing Smith towards goal. The ball bounced off the inside of the post, and despite Mark Phillips' best efforts the assistant referee flagged to say the ball had gone over the line.
Smith then had to be at his best to keep the deficit down to one as he tipped Marsh's curling effort behind for a corner.
At the other end, it was Tomlin who looked most likely to level things up for Blues. He took Michael Timlin's pass in his stride and forced an unorthodox save from Oxford goalkeeper Ryan Clarke.
Blues began the second-half on the front foot and with ten minutes gone they were level. Timlin's cross-field ball wasn't dealt with by defender Luke O'Brien and Clohessy smashed home the loose ball.
And it was so nearly 3-2 to Blues minutes later. Clohessy was again involved as this time he whipped in an excellent cross that was met by the head of Tomlin - but he saw his header hit the crossbar.
That miss didn't prove too costly though as Blues went ahead from their next attack. Corr played the ball into the feet of Tomlin, who laid the ball back for his strike partner to curl the ball with his right foot into the far corner from 18-yards.
Oxford responded well, and were almost level as twice in quick succession Blues almost put through their own net.
The home side threw everything they could at Blues, making three changes in quick succession and with 88 minutes gone they were level. A near-post corner was flicked on and Rigg was on hand to head past Smith.
Sturrock then opted to sub Smith for Daniel Bentley with penalties looming, and he was again the hero as he saved Alfie Potter's penalty and Blues converted all of theirs to win 5-3.
Blues now face a two legged tie with Leyton Orient for the right to play at Wembley.
Blues: Smith (Bentley); Clohessy, Cresswell, Phillips, Barker; Hurst, Timlin, Woodyard (Prosser), Straker; Corr (Benyon), Tomlin. Subs not used: Martin, Leonard.
Att: 2,882 (356 away fans)