Tony Smith's side will now face defending champions Leeds Rhinos in their first ever Grand Final at Old Trafford next Saturday.
The hosts took the lead after 11 minutes as Tom Makinson went over, but he was unable to convert his own try.
Francis Meli scored the Saints' second try of an exhilarating first half but Makinson was again off target with the conversion.
However, he kicked between the posts on 35 minutes after Paul Wellens went over during a dominant spell for the home side.
That looked to have given the Saints a comfortable lead going into the break, but Simon Grix touched down two minutes before the whistle to keep the visitors in contention. Hodgson then kicked over for the second time to make it 14-12 at half time.
If it was a narrow opening 40 minutes between the two sides then it was a different story in the second as Warrington went into overdrive.
They were made to endure a nervy final 10 minutes when Meli got his second try of the match, but Hodgson kicked over again to cap the triumph.