City's David Wetherall and Dean Windass were also keen to show they have lost none of their skills, and despite the lack of goals there was no shortage of enterprise and nothing boring about the game.
Ex-Bradford favourite Beagrie was quick to display his repertoire of skills, carving open the City defence to create a chance for Cleveland Taylor which went begging.
The Bantams began to settle, and after Danny Cadamarteri saw a shot skid past the post, midfielder Lewis Emmanuel's snap-shot was only just wide of the mark.
Windass then had a great header stopped on the line by Iron defender Cliff Byrne from Bobby Petta's pin-point cross.
That early push from the visitors soon became little more than a distant memory as Scunthorpe began to take control, and a brilliant run by Taylor saw his cross picked up Billy Sharp who put the ball over the top.
Beagrie than cracked in a fine left-foot shot which Donovan Ricketts saved at the foot of the post.
Veteran Beagrie, now in his 41st year, was again the architect in two further moves, setting up Andy Keogh to beat Wetherall and forcing another fine save from Ricketts. He then provided another piece of skill before driving straight at the keeper.
On the interval Marc Bridge-Wilkinson got free of the home defence, but his effort was straight at Tommy Evans.
Windass drove over as City opened a second spell on the attack, but then were left holding their breath when the referee waved aside strong shouts for a penalty when Petta looked to bring down Neil MacKenzie.
With 15 minutes left Cadamarteri forced Evans into a fine save, but Scunthorpe almost snatched the points when substitute Matthew Sparrow struck the woodwork after a Taylor shot was blocked and MacKenzie's follow-up was cleared off the line.