The result also dented the promotion bid of the free-scoring Tykes, who had netted five goals in each of their last two games.
Sodje, the former Nigerian international defender, stooped low to head home after a shot from West Ham loanee Chris Cohen had rebounded off keeper Scott Flinders.
Yeovil's defenders knew they would be in for a tough afternoon, but their cause was helped by the non-appearance of Martin Devaney due to illness, and the comparative ineffectiveness of Paul Hayes. Both players were Yeovil targets last summer, and both have been frequently on the scoresheet.
The Glovers have a habit of conceding early goals, and they did it again. In the 15th minute Robbie Williams was left unmarked at the far post to head in a Bobby Hassell cross from the right.
Yeovil had their moments, with Matt Harrold bringing one superb save from Flinders.
However they should have gone further behind just before the break when Paul Reid broke the home offside trap and had only keeper Steve Collis to beat. His lob was poor and went well wide.
Yeovil had just the start to the second half that they needed.
Inside the first minute David Poole was put through by Lee Johnson and finished well. The ex-Manchester United youngster had made only one previous start and it was his first senior goal.
Chris Cohen and Nathan Jones also went close before Sodje's winner.