Bevington's 20-metre run in after fine work from Dan Biggar, Sam Lewis and Tom Grabham saw the Ospreys lead 10-8 at the close of the first 40 minutes but Bath were the only team to trouble the scoreboard in the second period as they added three further tries to Matt Banahan's first-half effort.
British & Irish Lions stars Richard Hibbard and Ian Evans gained their first involvement since returning from the successful tour of Australia, while former Wales skipper Ryan Jones was another to come on at half-time ahead of Friday's RaboDirect PRO12 opener against Treviso. Hibbard played for exactly 20 minutes on his return to action, while Evans had his short spell ended with blood dripping from a mouth wound.
Biggar and opposite number George Ford exchanged early penalties on a night on which slippery conditions made attacking rugby difficult but it was Bath who were on top for much of the early exchanges.
The Ospreys were twice fortunate to survive with their line intact inside the first 10 minutes as Bath blew significant chances to grab the game's opening try. Fijian wing Semesa Rokoduguni took the wrong option in deciding to switch with full back Ollie Devoto when staying out wide would most likely have resulted in a score, and then No8 Leroy Huston spilled the ball on the line after the Ospreys pack had been driven backwards at a close-range lineout.
Yet while Bath dominated the first quarter, the Ospreys stayed strong defensively and eventually broke out of their own half courtesy of a typically incisive break from Biggar. The Wales No10 sliced into Bath territory before chipping over Devoto and forcing Banahan to clear his lines level with the 22. The momentum was shortlived, though, as a loose lineout handed Bath back possession.
The hosts eventually crossed for the first try just past the 20-minute mark as Kyle Eastmond's floated pass saw Banahan touch down in the left-hand corner. Ross Jones and Grabham both worked hard to stop the giant England wing in his tracks but, without the assistance of a TMO, referee Luke Pearce gave Bath the benefit of the doubt for an 8-3 lead.
Ford pushed his difficult conversion attempt across the face of the posts but the Ospreys could have few complaints about being behind after the first quarter. They weren't behind at the half-time break, though, as a sublime score handed them a two-point advantage with half an hour gone.
Yet again Biggar was at the heart of the move, with his flat pass to openside flanker Lewis on his own 10-metre line creating the initial impetus. Lewis in turn found Grabham, who sprinted into the 22 before offloading to the supporting Bevington just as Bath threatened to bring the phase to an end. Bevington showed an outstanding turn of pace for a loose-head as he raced home to touch down underneath the posts.
Biggar's straightforward conversion pushed the Ospreys in front for the first time on the night and the lead could even had been five points had his first penalty attempt not fallen short from fully 55 metres with the final play of the half.
Tandy brought on Hibbard, Ryan Jones, Duncan Jones and Jonathan Spratt at the interval but it was Bath who began the second period the brighter thanks to an early try from Huston. The New Zealand-born Australian backrower capitalised on Ford's mini break as he powered through two weak tackles from five metres out.
Ford's conversion saw Bath move 15-10 ahead and things got worse for the Ospreys shortly afterwards as Rokoduguni slipped through Ryan Jones' attempted tackle for a third Bath try after 51 minutes. Rokoduguni had been brought down bravely by Ben John earlier on the move but he was soon back on his feet to cut inside from 20 metres out as Jones went a little too high after Bath had kept the move alive with continuous quick ball.
Devoto added a further gloss to the scoreline when he dived over following impressive phase play with four minutes to play to leave the Ospreys with too much to do to secure a repeat of last week's late win over Worcester.
Ospreys: Ross Jones; Tom Grabham, Ben John, Ashley Beck, Eli Walker, Dan Biggar, Tito Tebaldi; Ryan Bevington, Scott Baldwin, Dmitri Arhip, Sam Williams, James King, Tom Smith (captain),Sam Lewis, Dan Baker
Replacements: Matthew Dwyer, Duncan Jones, Joe Rees, Ian Evans, Ryan Jones, Morgan Allen, Sam Davies, Jonathan Spratt, Tom Isaacs, Matthew Morgan, Arthur Ellis, Richard Hibbard, Jake Cole