Christophe Berra’s fourth goal of the season sent the 1000 strong travelling Blue Army home happy.
The Scotland international volleyed the ball into the roof of the net seven minutes before the break to keep Town firmly in the Play-Off picture.
Daryl Murphy was close to adding to the lead after the interval, with Aaron Cresswell sending a late drive just wide as Blues go into Saturday’s game against FA Cup holders Wigan on a winning note and just four points off the top six.
Town made four changes to the side that went down at Middlesbrough at the weekend, Luke Hyam, Paul Anderson and Stephen Hunt all coming into midfield with Sylvan Ebanks-Blake handed his first Championship start up front.
Ishmael Miller had a header deflected wide in the opening minute, Tom Lawrence then going close with a powerful drive from 25 yards as Yeovil started brightly.
Hunt’s cross in Town’s first opening evaded Ebanks-Blake, Marek Stech in the home goal gathering easily, while at the other end Luke Ayling’s deflected effort was dealt with equally as comfortably by Dean Gerken.
Good work by Anderson carved out an opportunity for Murphy inside the home box but the Republic of Ireland international shot high and wide.
Hunt almost found Ebanks-Blake with a reverse pass on the edge of the area in an even first half hour before Hyam picked up the game’s first yellow card for a foul on Duane Holmes.
Anderson was again the architect of another chance for Blues, his cross from the left just too high for Ebanks-Blake, then the wideman linked up with Murphy to set up Ebanks-Blake for a shot that was deflected wide by Byron Webster.
Murphy headed wide from the resultant corner as Town pressed for the opener and it came on 38 minutes, Tommy Smith headed on from Hunt’s corner and Berra forced the ball into the net from close range to give Blues the advantage at the break.
The Glovers made two changes at half-time, with front two James Hayter and Miller replaced by Sam Hoskins and Kieffer Moore.
Ruben Palazuelos had a shot blocked by Hyam on the edge of the box as Town kept the home side at bay, while Ebanks-Blake tested Stech with a right foot effort.
Hunt became the second Blue to be booked, Jonny Williams then introduced on the hour in place of the Republic of Ireland international, with Tyrone Mings on for Ebanks-Blake soon after.
Gerken had to be alert to keep out Moore after the substitute had got on the end of a long ball, Joe Edwards booked for a dive seconds later.
Town were inches away from a second on 68 minutes, Cresswell’s free-kick found Murphy but he couldn’t force the ball past Stech on the line.
Yeovil made a final change with Adam Morgan on for Holmes, Cresswell’s fierce cross belted clear by Webster.
Williams provided a threat working off Murphy and almost found a way to goal as the game entered the last 10 minutes, then Murphy fed the supporting Anderson but he couldn’t control his shot.
Cresswell was close with a left foot effort, then Stech was at full stretch to save from Cole Skuse, Mings heading the resulting corner straight at the ‘keeper but Town had a lucky escape in added on time when Moore’s thunderous left foot effort hit the inside of the post and bounced to safety.
There was still time for Murphy to test Stech but Berra’s strike proved the difference.