Eastbourne won for the fourth time in five matches thanks largely to the return to form of stand-in captain Callum Jackson.
Jackson took three catches from behind the wicket before top-scoring with the bat to end a run of three consecutive ducks for the Sussex man.
He won the toss and elected to put the hosts into bat and Ben Speake looked to have got Three Bridges off to a good start with a that included four boundaries. He was dismissed on 24 before fellow opener Bradley Gayler went for 16 and Richard Webber was out for nought.
Joseph Ludlow (35) and George Garton (64) put them into what looked like a decent position and they duly declared on 209.
David Twine was the pick of the bowlers with three wickets, while Jacob Smith continued his good form with two scalps form his seven overs.
Jackson (48) fell just short of his half century in reply for the visitors but he will pleased after enduring a tough time of late.
Luke Tomsett scored 40 to put Eastbourne in control and the partnership of Smith (25*) and Twine (37*) saw them reach their target in the 50th over with two wickets to spare.
Any threat of relegation is quickly fading as Eastbourne find themselves firmly in mid-table after this result. They are now in sixth place and 59 points outside the bottom two.
They have also closed the gap significantly on the teams above them and are just seven points behind Horsham in fifth.
If they can string a few more wins together against teams towards the top end of the league in the second half of the season they could find themselves in uncharted territory.
With eight matches remaining they are just 29 points off of top spot.