Cheltenham 0 Scunthorpe United 2
The 38-year old former Everton player made both goals as Brian Laws' team, who struggled to avoid relegation last season, continued their flying start to the campaign.
It could have been a different story had Cheltenham been awarded a fifth minute penalty when JJ Melligan tripped over goalkeeper Paul Musselwhite.
Referee Keith Stroud ruled that no foul had been committed much to the annoyance of the home crowd.
Five minutes later the visitors took the lead when Beagrie beat Brian Wilson and crossed from the left. Cleveland Taylor headed the ball across goal and John
Brough's headed clearance fell straight to Richard Kell on the edge of the box.
The Scunthorpe midfielder let fly with a first time volley from the edge of the box that flew into the top right-hand corner of Shane Higgs' net.
After that the first half proved to be an open, competitive contest and although Scunthorpe had the majority of the ball, Cheltenham created the better chances.
Brough shot just wide from a Jamie Victory cross then just failed to connect with a good cross from Melligan as Cheltenham pressed hard for an equaliser.
The home side applied intense pressure in the minutes leading up to half-time with Musselwhite making a diving save from a Brough header then stretching to touch a goalbound 25-yard free-kick from Melligan over the bar.
Cheltenham should have equalised in the first minute of the second half when a wonderful piece of skill from Kayode Odejayi took him around Musselwhite, but the big striker fired his shot against the post.
Higgs was forced to make a double save from Cleveland Taylor and Matt Bailey midway through the second period, but most of the attacking after the break was done by the home side.
However, try as they did the Robins could not break down a determined Scunthorpe defence, and the points were wrapped up two minutes from time when Beagrie got away on the left and crossed for loan signing Andy Keogh to score with a close-range header.