Izzy Iriekpen's first-half header followed by a Terrell Forbes own goal kept the Iron among the early pace-setters in a match they dominated from start to finish.
They could have been 3-0 up in as early as the sixth minute after an electric start to the game.
After on-loan centre-back Krystian Pearce headed over the bar from a corner within the first 50 seconds, Paul Hayes was denied by the inside of the post after curling his shot goalwards from a tight angle.
The Scunthorpe striker was then desperately unlucky to see a powerful right-foot shot beaten away by visiting goalkeeper Asmir Begovic from point-blank range after being teed up by a mis-hit effort from Matt Sparrow.
With the home side making all the running, it looked only a matter of time until the forged ahead and so it proved.
Yet having been forced to play second fiddle to some excellent attacking football, the goal the Glovers did finally concede, in the 27th minute, was a soft one.
Grant McCann swung in a deep cross to the far post from Scunthorpe's eight corner of the game and skipper Iriekpen met the ball with a strong header which looped over Begovic and into the far corner of the net.
Despite having been on the back foot, Yeovil rallied.
And they ended the half the stronger of the two teams with United keeper Joe Murphy forced into action to turn a Paul Warne effort around the post and then bravely diving at the feet of midfielder Darren Way at the second attempt to keep his side in front.
Seemingly fired up by a half-time pep talk from manager Nigel Adkins, Scunthorpe regained the ascendancy after the interval.
Sparrow flashed a 20-yard drive over the top before Begovic had to be alert to tip a deflected Martyn Woolford cross over the bar.
The home side doubled their advantage thanks to another well-worked move in the 62nd minute.
Cliff Byrne's deep cross was headed back into the middle by Woolford and midfielder McCann's scuffed shot hit the back of the net via the body of defender Forbes.
The goal signalled the end of the match as a contest as Scunthorpe relaxed somewhat, though Sparrow came close with a rasping effort and McCann had a free-kick held by Begovic as the Iron played out time.