It was a second successive away win for the impressive Glovers, leaving struggling Scunthorpe anchored at the foot of the League One table without a point from their opening three games.
Both teams cancelled each other out in the early stages before the Iron went close after 25 minutes, centre-back David Mirfin meet a left-wing corner from Josh Walker with a fine header which was cleared off the line by Ed Upson.
But it was Yeovil who made the breakthrough after 37 minutes when Keanu Marsh-Brown was left unmarked to run into the box down the left and drill in a low shot which beat Sam Slocombe at his near post.
Scunthorpe responded well and came close to an equaliser just before half-time when a free-kick from Walker was turned over the top at full stretch by `keeper Marek Stech.
Yet Yeovil took a firm grip on the game five minutes into the second half with a move which sliced through the heart of the home defence for striker Reuben Reid to make it 2-0 with his first goal of the season from close range.
Scunthorpe were denied three times by good saves from Stech as they tried to get back into the game, keeping out well-struck efforts from Bobby Grant, Mark Duffy and substitute Connor Jennings.
But substitute Gozie Ugwu had the final say for Yeovil, striking twice in the closing minutes with the home side collapsing defensively as a rain storm descended on Glanford Park.
First Ugwu tapped home from close range after Scunthorpe had lost possession in their own box, then, in stoppage time, he rounded keeper Slocombe for a fine solo effort.