Quakers gave a good account of themselves, but Beestin was more clinical when the chances came along.
Former Darlington striker Mark Beck was involved early on for Scunthorpe, flicking the ball on for Chris Wreh in the Darlington penalty area, but the ball was cleared.
Quakers responded well, and went close with a left-foot shot by Scott Barrow from 25 yards that flew just past the right-hand post.
Hazeem Bakre then made a great run up the middle, but was stopped in the Scunthorpe area.
Scunthorpe took the lead with their first serious attack on eight minutes. A clearance by the Quakers defence went to Beestin, who played a one-two with Wreh, then beat Peter Jameson with a right-foot shot from 12 yards.
It was nearly 2-0 on 12 minutes when Callum Roberts broke up the left, got to the byline and pulled the ball back for Beeston, who side-footed against the post.
But Quakers responded with a good diagonal ball by Toby Lees for Scott Barrow, who then set up Hazeem Bakre to put in a low shot that Fitzsimons saved down to his left.
But it was 2-0 on 28 minutes. Beestin again received the ball about 25 yards out, beat a defender, and then struck a low right-foot shot past Jameson into the bottom left corner of the net for his second of the game.
He nearly scored his hat-trick on 31 minutes. He got away from the Quakers defence to pick up a through ball, but fortunately Jameson managed to get his hand to the ball and deflect it around the post.
Quakers started the second half well and had a chance when a free-kick was floated in from the left by Scott Barrow for Main to set up Will Flint, who fired over the top.
Quakers then had another chance when Cornish threaded the ball through for Main to control, but Fitzsimons blocked his shot.
Right-back Ben Hedley decided to chance his luck on 58 minutes as the Iron defence back-pedalled, and his low shot was saved by Fitzsimons at the foot of his post.
Beestin was always a danger, and again he found space on the edge of the area to fire in a low right-foot shot that Jameson saved.
Quakers had a half-chance from a corner by Caden Kelly, but Jack Maskell couldn’t turn on the ball on the six-yard line.
