Barring any unthinkable scores in the remaining games this weekend, Nathan Brown's men appear set for a play-off meeting with Hull KR, while Hull must wait on other results to see whether their likely clash with Catalan Dragons will be played in England or France.
Things were only ever going to go one way by the Humber as the in-form Saints shone, building up a four-try lead which they took to the break thanks to scores from Jon Wilkin, Josh Jones, Swift and Willie Manu.
Hull would respond through Richard Whiting, but Francis Meli gave Saints an unassailable lead which was added to by Louie McCarthy-Scarsbrook. Danny Tickle added a further Hull consolation.
The home side had brought back Aaron Heremaia but were without the injured Ben Crooks, Andy Lynch and Gareth Ellis, but the real headline inclusion was that of Saints hooker James Roby.
Back after a two-month lay-off in time for the World Cup, his presence and performance was great news for club and country and Saints were clearly lifted by his presence.
They drew first blood, with Meli racing away and playing in Wilkin on his inside, with Johnny Lomax tagging the extras.
Hull responded briefly through Jamie Shaul's run, but Jones made it two tries for Saints after a strong break from Swift.
Three tries were soon on the board as Swift had too much pace for Jason Crookes, while Manu haunted his former employers on the half-time whistle.
Hull needed a quick response and got one at the start of the second half when Jacob Miller sent Whiting in, but a 40-20 from former Black-and-White Jordan Turner put Saints back on the front foot and allowed Meli to squeeze in.
A penalty-ridden spell followed before Swift added his second of the night, taking in Lomax's excellent cross-field kick, with Lomax tagging on to take the score out to 32-6.
Tickle, heading out of Hull to go to Widnes next season, responded from close range before McCarthy-Scarsbrook, a former Hull academy player, rounded things off.