Yeates double gave the Spitfires an unlikely three points on the road - watch match highlights here.
The Eastleigh midfielder netted either side of half-time before Danny Whitehead pulled one back late on.
It was the first time Eastleigh had won away since September and came at a good time after a hugely disappointing home defeat to Solihull Moors last Tuesday.
Yeates said: "It's a big win because after the result we had, people weren't really giving us a chance. This league is so strange.
"We know what we've got in that dressing room, even with injuries, we felt the squad we had today was more than capable of doing what we did. People on the outside might see it as a surprise result but we didn't.
"I think what's frustrating is seeing what happened on Tuesday night and then seeing us go out and perform like that.
"We've got as good a group as anyone in the league really."