The visitors opened the scoring after three minutes of this scrappy North Lancs League Two fixture.
They chased down a long ball and, having won the subsequent lineout, scored under the posts.
Bury replied 10 minutes later when, from a lineout 15 metres from the try line, lock forward James Swinburn crashed over for an unconverted try. Eagle replied in the 25th minute when they worked the blind side and poor covering by the Bury defence saw them score another unconverted try. Bury replied almost immediately, opting for the set scrum after being awarded a penalty.
The ball was moved to stand-off Lawrence Shedwick who sold a dummy, grounded under the sticks and converted his own try. The last score by Bury was a well worked cross field move which saw right wing Dan Scanlon score an unconverted try in the corner.
Eagle completed the first period with a succession of rucks and mauls, which saw them score an unconverted try, but Bury went in to the interval two points ahead.
Bury lost the services of Shedwick and winger Sam Ware in the second half and this changed the dynamics of the side.
Bury conceded the first of two tries after 15 minutes when Eagle muscled their way over.
The hosts added to their tally 10 minutes later when a mix up between a Bury wing and full-back allowed them to pick up and score a converted effort. Bury pressed hard for the last 15 minutes and could have scored on two occasions, but the referee deemed their efforts to be held up, even though Bury had crossed the try line. On Saturday, Bury entertain Newton-le-Willows at the Radcliffe Road ground, kick off 3pm.