It came at an important time as it put eight points between themselves and Cheltenham. With Gillingham also losing, manager Russell Slade is confident his team will not be dragged into a serious relegation dogfight.
Kirk embarked on a tremendous 60-yard run in the eighth minute to set up the opening goal. He appeared to lose control as he was about to pull the trigger, but a panicking Cheltenham defence contrived to put the ball into their own net off Alan Wright.
It gave Yeovil the impetus they needed and they could have had more goals. Instead, it was Cheltenham who had the best chance to draw level right on half-time.
They were awarded an 18-yard free-kick in a central position when Matthew Rose brought down Steven Gillespie. Wright had the chance to atone for his own goal, but fired into the defensive wall.
The Robins' first-half display was described as inept by manager Keith Downing but they perked up after the break, most of the danger coming from loan signing Steve Brooker, who is likely to return to Bristol City after one more match.
It was a typical piece of Brooker opportunism that brought the equaliser in the 64th minute.
Substitute Ashley Vincent got in a cross from the right and when skipper Terry Skiverton failed to clear, Brooker was handily placed at the far post to crack home a left-footed drive.
Yeovil won the game in the 74th minute. A throw-in on the right was not dealt with by the Cheltenham defence and Kirk cashed in to rifle home a ten-yard shot.
He should have had another in stoppage time, but completely in the clear and with the goal at his mercy he fired at the legs of keeper Shane Higgs.