The home side pressed early on and had a chance to take the lead through Ishmael Miller. His shot took a deflection and looked bound for goal, but Luke Steele was on hand to make the stop for Barnsley.
The visitors had a great chance to take the lead when Chris O'Grady raided forward into the box and managed to cut the ball back to substitute Reuben Noble-Lazarus, but his effort from close range went wide.
Yeovil threatened just before half time when Kevin Dawson fired a free kick at goal, but Steele was there to produce a good save to keep the score level.
After the break, Barnsley took the lead when O'Grady nipped in on a poor back-pass from Byron Webster and made no mistake in firing the ball past Marek Stech.
The visitors doubled their advantage minutes later when O'Grady turned provider this time. Lawrence found him on the edge of the area, and the midfielder drilled the ball past Stech with a fine strike.
However, hopes of a comeback were extinguished when O'Grady got his second of the contest as he beat the offside trap and rounded Stech to slot the ball home.
Barnsley rounded off their win when Dale Jennings bounded into the penalty area and fired past Stech.