The visitors, managed by ex-Town manager Paul Sturrock, snatched all three points thanks to a determined counterattacking performance and made the best of their limited attacking with James Berrett’s 58th minute goal the difference between the two teams.
Mark Cooper unsurprisingly elected to keep an unchanged line up after the superb win at Rochdale and the Robins went straight on the attack with Harry Toffolo charging down the left wing to put Yeovil under pressure but eventually the ball rolled out for a goalkick.
Stephen Kingsley was fortunate not to be shown a yellow card for hauling Byrne over just outside the penalty area and when Gladwin took the freekick, the ball eventually flew out for a corner when Smith’s shot was deflected behind in the 6th minute.
Town had another freekick in the 9th minute about 25 yards from goal but the visiting keeper Krysiak caught the ball cleanly.
The visitors were set up to stifle Town’s attacking play leaving just one player up front and the Robins continually probed in attack leading to two corners in the space of a minute which led to nothing as the match entered the 16th minute.
Nathan Bryne set up Obika with a great chance to score in the 19th minute after the Town wingback managed to get hold of a loose ball from a defensive header but Obika’s first time shot struck the sidenetting.
Town’s patient approach led to a chance for Obika who latched onto a cross by Gladwin but his powerful effort went wide in the 22nd minute.
Gladwin was getting plenty of the ball and he earned a corner when his shot from 25 yards ricocheted behind after a deflection and shortly afterwards Gladwin rattled the upright with a fine long range shot but the ball rebounded away from goal and was cleared.
Kingsley was cautioned for fouling Byrne again near the corner flag in the 28th minute but the when the resulting free kick was taken, the ball flew across the penalty area and was cleared. Two minutes later the Yeovil keeper spilled the ball which eventually reached Byrne on the edge of the area but his effort flew high over the crossbar.
Town continued to push forward and on 31 minutes, it was Obika’s turn to shoot from 20 yards after receiving a deflected pass but the keeper took his shot cleanly.
Yeovil threatened briefly and earned a corner from a misplaced defensive clearance and Foderingham did well to push away a powerful header by Kieffer Moore and the ball was cleared in the 41st minute and shortly afterwards Josh Sheehan fired in a wayward shot which flew wide of goal.
Town started another phase of attacking play without finding a final shot on goal before the whistle was blown with exactly 45 minutes played.
The first main action of the second half saw Byron Webster try and score with an audacious shot from 60 yards as tried to catch Foderingham off of his line but the ball landed on the roof of the net with the Town keeper backpedalling.
The half progressed much the same way as the first half with Town on the attack which led to Obika trying his luck from 20 yards his weak effort was easily saved by Krysiak. Jack Stephens threw his body in front of a shot to deflect the ball out for a corner which led to nothing.
Town allowed Yeovil too much time and space for a couple of minutes with some tentative play and eventually James Berrett gave the visitors the lead in the 58th minute after firing in a long range shot which beat Foderingham at his near post.
Yaser Kasim replaced Toffolo before play restarted and Town were then denied an equaliser when Arthurworrey cut out a goalbound shot by Obika with the keeper beaten. Town thought they had scored shortly afterwards when Smith’s close range shot struck the crossbar and the ball stayed out of the goal according to the assistant referee.
Michael Smith was by Andy Williams in the 63rd minute and Town were soon on the attack again but Yeovil continued to defend in numbers but eventually earned a freekick 20 yards or so from goal which saw Sheehan fire narrowly wide of goal and at the other end, Gladwin earned a corner for Town.
John Swift replaced Rodgers in the 73rd minute with Mark Cooper looking for some inspiration from midfield but the visitors were looking comfortable in defence soaking up the pressure.
Joel Grant found himself with time and space to shoot in the 78th minute but his effort went just wide and at the other end, John Swift tried his luck with a shot from 10 yards but that went into the side netting.
Swindon were getting more frustrated as the match wore on with misplaced passes and indecision in attack not helping their cause.
Josie Ugwu and Ajay Leitch-Smith replaced Moore and Grant in the 86th minute as the visitors looked to run the clock down.
Town simply could not break the visiting defence down and even when presented with a chance to shoot as the match entered added time, Swift hesitated and the ball eventually went harmlessly out for a goal kick.
The Robins were presented with a good chance from a free kick deep in added time but Kasim’s cross evaded everyone and the chance was gone.
Kasim had another shooting chance at the end of added time from a free kick but Krysiak pushed the ball out for a corner which was cleared just before the final whistle was blown to end a disappointing match for Mark Cooper’s men.