Dominic Solanke opened the scoring midway into the first half for his 18th goal of an excellent season, before the hosts turned the game around with goals from Olivier Kemen and Adam Armstrong, the first scored in controversial circumstances.
However, the young Blues regrouped at the break and were level after 52 minutes through Alex Kiwomya, before Jeremie Boga netted a sensational winner from 30 yards with 25 minutes remaining.
Blues coach Adi Viveash told chelseafc.com: "You have to remember the quality of the goals too. Even right at the end with Reece Mitchell's chance where we were all willing him to score after what happened last season in the quarter-final at Derby. We scrapped and fought and we mixed it up tonight against a team that play a bit differently to us. It was a tough game but the boys deserve to be in the semi-final."
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