United trailed to Luke Varney's goal at Gresty Road, but hit back to record their sixth straight win.
Sharp equalised with an instinctive finish from just inside the box, while Beckford hit his second stunner in as many games.
His goal was almost a carbon copy of his winner of his strike against Rotherham on Saturday, as he flicked the ball with his right foot before curling the ball into the far left corner with his left.
Sharp has now netted an impressive 24 times this season, with Jermaine Beckford popping up with a fantastic first half strike.
"Sharp got two more goals and could have had a hat-trick but for a good save from their keeper," beamed Adkins.
"He is on fire. He is working so hard for it that its almost untrue. He has to believe he is capable of 30 goals this season
"Beckford scored a wonder goal for us again, but I was pleased with his overall play. He was looking to get other players involved rather than trying to score a goal every time he gets the ball."
Although the win moved United a remarkable nine points clear at the top of League One, Adkins insists his side are thinking only of Saturday's trip to Brentford.
"We are delighted with what has happened but we are not going to get carried away," he insisted.
"It's great for our supporters to dream about being in the Championship next season. `
"We are going to take some stopping, but we have to keep working towards our set goals and targets.
"We have character and desire and passion to work for each other, and we also now have belief that things will go for us."
Crewe boss Dario Gradi admitted Scunthorpe were good value for his side, although he felt the Railwaymen lost their belief after Sharp's crucial second goal to make the score 302.
"It came down to the goal scorers and while Varney did well for us, Billy Sharp scored twice," he said.
"He was helped by the rest of his team-mates and Varney didn't get that support, as Mike Higdon didn't look like scoring.
"Sharp was a threat all night, he was busy without being quick but had good feet and can finish.
"I'm disappointed with all the goals they scored and although we were decent in the first half, we lost our fire once the third goal went in."