Saints started life without Jim Mallinder in the same fashion as his tenure ended, as Ospreys secured a bonus-point 32-15 win at the rain-soaked Liberty Stadium.
The Welsh region, who had scored six times on their way to a 43-32 victory at Franklin's Gardens eight days earlier, ran in three tries after half-time, two of which came from replacement Rhys Webb, as Saints' misery continued.
They had threatened a fightback after half-time as a try from Harry Mallinder and a penalty from Piers Francis cut the gap to three points at 11-8.
But Ospreys then pulled away, with Wales internationals Webb and Justin Tipuric doing the damage, before Reece Marshall grabbed what was barely a consolation try for Saints.
It means the green, black and gold have lost all four of their Champions Cup matches this season, shipping a try bonus point in each of them.
They have now suffered 10 defeats in their past 11 matches in all competitions as the search for a new director of rugby continues.
The trip to Swansea may have signalled the start of a new era, but there was no change on the field early on as Ospreys found gaps in the Saints rearguard.
Ben John made the initial break and the move ended with Dimitri Arhip scoring in the corner, with the prop punching the ball in delight after powering over.
Sam Davies missed the conversion, but Saints, who had missed several tackles in the build-up to the try, were already behind and needing a response.
They almost found the score to level when a slick move gave them numbers out wide, but Mallinder's offload was just not quite accurate enough for Ahsee Tuala.
But with Tuala having knocked the ball on before it went out of play, Saints had a scrum chance, winning a penalty against the head, allowing them to apply some pressure.
However, Ospreys turned on the power to resist an attempt at a lineout drive and Saints knocked the ball on, losing possession at the key moment.
And Ospreys soon made Saints pay as Davies landed a couple of penalties to take his team's tally up to 11 points inside the opening half an hour.
A huge hit from Mike Haywood in defence helped to turn the tide as Saints quickly won a penalty and returned to opposition territory, putting the squeeze on.
But Ospreys again defended ferociously, intercepting a pass and taking the heat off, ensuring they would retain their healthy lead heading into half-time.
The Welsh team had been largely dominant at scrum time and that theme continued early in the second period as Saints continued to struggle to retain any attacking momentum.
That was until Francis sent over a lovely crossfield kick and Tuala did superbly to rise and tap the ball down to Mallinder, who scored in the corner.
Francis missed the conversion, but he was soon slotting a penalty after Saints won a penalty at the breakdown.
Suddenly, the deficit was down to just three, but Ospreys came again and after a lovely offload from Davies, the door was unlocked, with Webb walking through it.
Davies added the extras to the half-time replacement's try, and Saints were 10 points down with 23 minutes remaining.
The away side reshuffled their backline, with Rob Horne and Francis withdrawn, possibly with a view to Saturday's clash with Exeter, and Ospreys soon took advantage.
Full-back Dan Evans flew through a gap and, a couple of offloads later, flanker Tipuric dived over for his team's third try.
And it wasn't long before the bonus-point score arrived as Webb showed good awareness to dot down.
Davies converted again to make it 32-8, with Saints staring at another sizeable defeat.
Hooker Marshall popped up to score before the end, with Mallinder adding the conversion, but it was scant consolation for Saints.
Ospreys: Evans; John (Webb 40), Fonotia (Beck 70), Watkin, Hassler; S Davies, Habberfield (Biggar 68); Smith (James 71), Baldwin (Otten 70), Arhip (Fia 64); B Davies; Wyn Jones (c) (Beard 70); Lydiate, Tipuric (McCusker 70), Cracknell.
Saints: Mallinder; Tuala, Horne (Pisi 64), Stephenson, Foden (c); Francis (Burrell 64), Groom (Reinach 57); Van Wyk (Ma'afu 48), Haywood (Marshall 68), Ford-Robinson (Hill 48); Ribbans, Paterson (Ratuniyarawa 70); Gibson, Ludlam, Harrison (Eadie 57).
Referee: Marius Mitrea (Italy)