The Premier League outfit recorded a disappointing result with a strong side at Plainmoor despite dominating the majority of proceedings against the League Two club
The Potters took the lead just two minutes before half-time, with Aaron Downes deflecting Matthew Etherington's effort past his own keeper, Michael Poke.
But, after the hosts had a few chances in the second half, Bodin's effort eluded Carlo Nash with just 11 minutes left to secure an unlikely draw.
| THE GOAL.COM 50: POSITIONS 50-4
|Our definitive countdown of the finest players from 2011-12 has commenced. Click here to view our slideshow of the stars who ranked 50-4 in our list!|
Tony Pulis also included Poland international Sebastian Boenisch, who may be close to sealing a move to the Britannia Stadium after a trial appearance.
The game opened in typical friendly fashion, with a lack of tempo and clear-cut chances. But, after a slow start, it was the Premier League side who had a golden opportunity to open the scoring. Etherington did well down the left-hand side before squaring a low pass to Crouch, but the England international fired well wide of the target.
Torquay had their first chance of the match shortly after, with Thomas Sorensen having to be on guard with a fingertip save to deny Danny Stevens after his low effort looked goalbound.
Stoke continued to dominate, with Ryan Shotton having his shot well saved by Poke after bursting inside the Torquay penalty area. But, with half-time approaching, Stoke took the lead in bizarre circumstances.
Shotton ran down the right-hand side and switched to the unmarked Etherington. The former Spurs man thundered an effort which looked to be going off target before striking Downes and finding its way into the net.
|40/1||Stoke City are 40/1 with Bet365 to win the 2012-13 FA Cup|
With more changes sucking any momentum out of the contest, Bodin's presence in the game was increasing, his free kick midway through the second half troubling substitute keeper Carlo Nash.
And it was Bodin's subsequent effort that got Torquay the equaliser. The striker cut in from the right, took aim and blasted an effort into the bottom right corner, leaving Nash with no chance whatsoever.
Despite an effort from Ashley Yeoman in injury-time, Stoke held on to secure a draw ahead of their Premier League opener against Reading on August 18.