The Saints moved three points clear of sixth-placed Hull FC with a 38-12 win over the club this evening.
Richard Whiting got Hull back into the match at the start of the second half, but four more scores for the Saints, including a second for Swift, opened up a comfortable lead.
Meanwhile, Widnes claimed their third consecutive win, beating Salford City Reds 24-4.
Marc Sneyd scored the only try of the first half just before the break to give the home side the lead at half time.
However, the Vikings fought back with four second-half tries, including a brace from Patrick Ah Van.
The result leaves Widnes ninth in the Super League table.
Results in full: Hull FC 12-38 St Helens, Salford City Reds 4-24 Widnes Vikings