Goals from Jay DaSilva and Tammy Abraham saw Chelsea go 2-0 up before Reading centre-back Axel Andersson pulled one back for the visitors.
There could’ve easily been more goals as Chelsea missed two penalties while Reading also failed to convert from 12 yards.
Reading began the game the brightest with Sam Smith latching on a long ball from Conor Davis only to see his effort go over Nathan Baxter’s goal from a tight angle.
Chelsea came to life on 24 minutes as their talisman Tammy Abraham blasted over from the edge of the box after fine work from playmaker Kyle Scott.
On the half hour mark, Chelsea went close again with winger Charlie Wakefield shooting narrowly of Reading goalkeeper’s Luke Southwood’s post. Mukhtar Ali and Wakefield also had shots flash just wide minutes later.
The game’s first controversial moment arrived after 40 minutes as Reading ‘s Andersson was judged to have fouled Wakefield inside the penalty area, TV replays showed Reading’s protests were justified as contact appeared to be just outside the box.
Southwood produced a fantastic save to keep out Abraham’s resulting spot kick to deny Chelsea a crucial lead just before the interval. Both players were again involved in more penalty drama as strong Chelsea appeals for a penalty were waved away by the referee Nicholas Kinseley after Abraham fell from a challenge with the on-rushing Royal’s stopper.
Chelsea began the second period the strongest with Scott blasting a half-volley over the bar from 18 yards out.
The host’s pressure did finally pay-off on 58 minutes, with Jay DaSilva tapping home a rebound from six-yards out after substitute Dujon Sterling’s shot was parried in to DaSilva’s path by the Reading goalkeeper.
The Blues doubled their lead as Abraham scored his 22nd goal of the season with an empathic header from an inviting Isaac Christie-Davies cross after 68 minutes.
Once the holders were 2-0 up Reading pushed forward for an equaliser and six minutes later Chelsea defender Trevoh Chalobah had to put in a last-ditch to tackle to deny Sam Smith.
With 12 minutes remaining Reading had the perfect opportunity to halve their deficit as Chelsea captain Jake Clarke-Salter brought down Danny Loader in the area. Reading winger Tyler Frost also fluffed his lines from the spot-kick as he blasted against the bar.
With five minutes left on the clock the young Royal’s nearly found an equaliser as a Frost cross flashed across the face of the goal and inches away from finding his teammates in the Chelsea box.
Reading’s search for a leveller exposed them to numerous Chelsea counter-attacks and deep into stoppage time a blistering Blues counter led to Dan Akinwumni bringing down the impressive Sterling inside the box and the Reading defender receiving his marching order following a second caution.
This time midfielder Ali stepped up for the West London side and his resulting spot-kick was comfortably saved by Southwood, joining Abraham and Frost on the failed penalty conversion’s list.
Southwood still had to pull out one more fantastic save to deny Scottish midfielder Ruben Sammut with last action of the game.
Chelsea advanced into the semi-finals for the seventh consecutive year in the FA Youth Cup were they will face Blackburn Rovers in a two-legged semi-final, while Reading bowed out at the quarter-final stage.