The Latics were beaten by Blackpool in May's play-off semi-finals but their new-look side edged out Swansea at the end of a frantic game.
Swansea performed like a team with every chance of pushing for promotion but they found Oldham goalkeeper Mark Crossley in good form and also allowed chances to go begging.
Oldham snatched their goals at the start and the end of the game, with both debutant strikers getting on the scoresheet.
Ex-England man Michael Ricketts was first to break through after Davies burst into the box and was hauled down by Swansea captain Alan Tate.
There were less than three minutes on the clock as Ricketts stepped up for the penalty, and he drove his kick high to the right of keeper Dorus de Vries.
Swansea went desperately close to a quick equaliser when Andy Robinson hit the foot of the post from 20 yards with a thunderbolt shot.
Some strong tackles ensured there was action on the pitch before Oldham manager John Sheridan's furious reaction to a tackle on loan signing Neil Kilkenny endured he was sent to the stands after less than 20 minutes.
Crossley made saves either side of half-time, denying Robinson and then doing superbly to tip away a 25-yard drive from Spanish defender Angel Rangel.
But Swansea were level on 55 minutes when Jason Scotland marked his impressive debut by finding space on the edge of the box and finishing with style in the bottom corner.
Swansea went on to create several more openings, with Crossley thwarting Paul Anderson and Ferrie Bodde and Kristian O'Leary heading off-target.
Oldham's Andy Liddell had also gone close before Davies grabbed the glory, netting with a close-range header from Deane Smalley's cross in stoppage time.