A Bobby Reid brace sandwiched Hordur Magnusson’s header to earn the second tier side victory in Somerset.
Olufela Olomola replied for Town in the second period with a beautiful left-footed shot from 25 yards but it proved to be a consolation.
Darren Way made one change to his starting line-up with Swansea City loanee Keston Davies, who signed on a season-long loan on Friday, replacing the injured Stephane Zubar in the heart of the Glovers’ defence.
The 20-year-old had the City’s record signing Famara Diedhiou to contend with and he kept the Senegal international quiet in the opening exchanges as the visitors struggled to breakdown Town’s stubborn backline.
Yeovil had the game’s first chances through Connor Smith’s long range effort and an Otis Khan free kick but City showed their Sky Bet Championship quality with three goals in quick succession.
Iceland international Magnusson’s spiralling long throw found the head of defensive partner Aden Flint who flicked on for Reid to tuck the ball away from close range.
Flint was in the midst of the action moments later, heading Jamie Paterson’s deep set-piece into the area and Magnusson rose above goalkeeper Jonny Maddison to nod into an unguarded net.
Two became three on 28 minutes through Bristol-born Reid who stroked home Republic of Ireland winger Callum O’Dowda’s pullback for his second of the match.
Former Oxford United man O’Dowda almost made it four before half-time but his curling shot, after a sweeping Robins counter-attack, whistled past the far post.
Southampton loanee Olomola was introduced at the break as Yeovil switched to a 4-4-2 formation and the young forward caused havoc amongst the Bristol City ranks from the off, breaking away from their back four before Joe Bryan recovered to make a last-ditch challenge.
Town fought hard for a way back into the contest and almost got what they merited. When Frank Fielding spilled a cross from the right, Khan picked up the loose ball, nudged it to his right but could only find the feet of the away stopper.
Wide man Browne’s venomous drive tested Fielding’s reactions once more before Maddison needed to be at his best to prevent Reid from sealing his hat-trick.
Then Olomola reduced the deficit with 14 minutes remaining. The 19-year-old picked up the ball some way from the goal before smashing a sublime effort past the helpless dive of Fielding to make the final score more respectable.
Yeovil Town: Maddison (Trialist 70), Mugabi (Trialist 70), N.Smith (Sowunmi 70), Davies (Trialist 70), Dickson (Trialist 70), Bailey (Trialist 70), Gray (Trialist 70), C.Smith (Olomola 46), Browne (Trialist 70), Khan (Trialist 70), Zoko.
Bristol City: Fielding, Pisano (Golbourne 66), Flint, Magnusson (Moore 57), Bryan (Pack 66), O’Dowda (Morton 85), Brownhill, K.Smith (J.Smith 85), Paterson (De Girolamo 78), Reid (Edwards 78), Diedhiou (Hinds 57).