The 35-year-old former Southampton, Derby and Leicester star played a major part in two first-half goals which inflicted a second successive home defeat on second-placed Vale.
And in doing so, Exeter consolidated their place in the play-off places and moved to within four points of the third automatic promotion slot.
Tisdale said: "It was a very pleasing performance and result and I thought all of our players were strong and did their jobs. But Matt Oakley was the pick of the bunch tonight. His quality and expertise on the ball shone through and that's what class players can do.
"We were the better side for the opening 15 minutes and when you go ahead you can afford to defend deep, which was what we did. I thought we played a very sensible and pragmatic game. We defended very well as a team and our goalkeeper (Artur Krysiak) was big and strong when he was needed.
"When you defend deep you need your goalkeeper to come for crosses and he did that excellently. It's a good result and pleasing to bounce back from losing at Burton, but we've got another tough game against Northampton on Saturday and we will prepare for that."
Vale boss Micky Adams said: "It was a disappointing and frustrating night for us and I suppose we got what we deserved - nothing.
"We just didn't get going. We are a free-scoring side who have stopped scoring at the moment and the reason for that is we aren't getting into the right areas.
"At 2-0 down we had to chase the game and I made the three substitutions to try to find a spark, but I didn't get one.
"I thought Exeter worked harder than us and out-battled us and that doesn't agree with me too much. The biggest thing was the crowd stuck with us and what we have to do now is dust ourselves down, pick ourselves up and go again."