He poked the ball home following a corner after seven minutes, and he finished off a superb counter-attack after the break to seal the win.
But although a host of clubs have been watching Sharp and his strike partner Andy Keogh, with Wolves boss Mick McCarthy publically declaring his intention to bid for both, Adkins is not planning on either leaving in the January transfer window.
"We have scouts out ourselves looking for players. We are interested in buying players and not selling them," he declared.
"Although Sharp got the second goal, a lot of credit goes to Keogh and Cleveland Taylor who set it up.
"Taylor ran 70 yards to get in the cross. It summed up our performance which was superb.
"We moved and passed the ball well and committed people to attack, the pace and everything connected with it was superb."
Yeovil manager Russell Slade admitted the Iron were good value for the three points.
"For the first 25 minutes I thought Scunthorpe were running it," he admitted.
"It wasn't until I switched our formation to 4-4-2 that I felt we were getting into things, and before that time Scunthorpe had three or four chances to get a second goal.
"We managed to stay in the game but the second goal really killed us, it came from a mistake which led to them breaking down the right."