Winger Rhys Browne netted for the second home game in a row but midfielder Luke McCormick levelled in first half stoppage time to earn the Blues a share of the spoils before spot-kicks ensued.
Chelsea goalscorer McCormick saw his saved by Artur Krysiak with every other penalty converted with Yeovil winning 5-3.
Darren Way made six changes to his side following Saturday’s draw with Barnet.
Browne and Sam Surridge were added to the Glovers attack and Sid Nelson returned to partner captain Nathan Smith at centre-back.
The duo of Alefe Santos and Matt Worthington formed the heart of the home midfield, while Tom James also earned a recall.
It was clear from the outset Chelsea’s aim was to pass the ball around with slickness and Yeovil’s determination to disrupt that in the early stages proved effective.
The hosts pressed high up the field, getting in the faces of their young opponents and their energetic style provided Tom James with an opportunity to strike from distance but he couldn’t keep his dipping volley down.
Otis Khan curled a free kick just wide soon after and Worthington lashed a first-time shot over from 25 yards in what was a quiet quarter of an hour on the clearcut chances front.
The former acted as the provider for Town’s next two efforts which saw Nelson and Bevis Mugabi head over before delivering the corner which created the opener.
Surridge connected with a firm header and Browne inadvertently knocked the ball beyond Jamie Cumming into the bottom corner.
The Glovers’ lead only lasted 12 minutes as Chelsea restored parity completely against the run of play.
In their first venture deep into Yeovil territory, wing-back Reece James’ fizzing cross was glanced goalwards by Martell Taylor-Crossdale, forcing Krysiak into an instinctive stop.
However, the Polish keeper could only palm into the air and McCormick reacted quickest to tap in.
Krysiak kept the score at 1-1 on the stroke of half-time, saving expertly from Jacob Maddox.
The ex-Bristol City youngster picked up Mugabi’s loose pass and his curling attempt towards the bottom was tipped behind by Town’s number one.
A bright beginning to the second half saw Reece James arrow a shot over on the angle and at the other end, his namesake Tom crossed for Browne who hit over on the turn.
Taylor-Crossdale fired low at Krysiak on 60 minutes before Jake Gray and Mugabi went close for the Green and Whites.
Former Luton Town man Gray fierce strike was acrobatically tipped over by Cumming and Mugabi’s header from the following corner skimmed off the top of the crossbar.
Khan was next to sting the palms of England youth international Cumming with a driven effort, the last real talking point ahead of a tense ABBA shootout.
Santos, Surridge, Khan, Olufela Olomola and Francois Zoko all dispatched from 12 yards with aplomb and McCormick’s miss for Chelsea meant two points went to Way’s side.
Yeovil Town: Krysiak, Mugabi, N.Smith (Davies 67), Nelson, T.James, Gray (Zoko 82), Santos, C.Smith, Khan, Surridge, Browne (Olomola 64).
Bookings: Santos 42, Browne 52.
Not used: Maddison, Sowunmi, C.Smith, Bailey.
Chelsea U21: Cumming, Colley, Nartey (Dasilva 77), Chalobah, Grant, R.James (Muheim 90), Maddox, Sammut, McCormick, Grant, Hazard (St Clair 62), Taylor-Crossdale.
Bookings: McCormick 80.
Not used: Tie, Castillo, Brown, Uwakwe.