The Australian's score completed a morale-boosting win in a pre-season friendly watched by a respectable crowd of 852 at Bloomfield Road.
"They would be hard to please if they didn't enjoy that," said the Blackpool coach Mark Lee, who now has an indication of what his team might achieve when the serious business begins in National League Two.
Saints fielded seven players who figured in their first team last season and it was those who did the damage as they built a 16-4 half-time lead.
Powerful Kiwi centre Gray Viane set up Ian Hardman for the first try, and Hardman's second came from a superb pass by Scott Moore, the 17-year- old stand-off who then scored the third try.
The honour of scoring Blackpool's first points at their new home went to Eric Andrews, before Gary Smith went over at the start of the second half. When Martin Gambles scored a try which Liam Bretherton converted, the Panthers were within two points, and the stage was set for Godbee's dramatic late winner.
Blackpool: Arnold, Salmon, Bretherton, Godbee, Andrews, Hough, Gambles, Molloy, Ramsdale, Parry, Leigh, G Smith, Barton.
St Helens: Hardman, Langley, Viane, Littler, Feaunati, Moore, M Smith, Leyland, Bostock, Terry, Cooper, Clough, Forber.
Referee: P Bentham (Warrington).Reuse content