Striker James Walker ran tirelessly on his debut for the visitors but clear-cut chances were few and far between in a dour first half.
However, there was more action at both ends in the second period as both sides struck the woodwork.
Nathan Smith fired a long-range shot against the bar for Yeovil in the 54th minute before Gillingham's Curtis Weston rounded Alex McCarthy and hit the post two minutes later.
Yeovil piled on the pressure in the closing stages but Gillingham also came close when substitute Simeon Jackson headed over.
Source: Team Talk
Source: Team Talk