The England standoff chased down a Brett Morris kick after the NSW winger busted the Tigers' line.
Gerard Beale crossed six minutes later when Morris skilfully tapped down a Widdop kick and the playmaker scored his double on the half-hour when Mitch Rein broke out of dummy-half and toed inside.
In the 36th minute Adam Quinlan had a try disallowed for obstruction before Tim Simona was also curiously denied a four-pointer.
The Dragons took full advantage of that favourable call when Jason Nightingale produced a classic finish to score and St George Illawarra went to the sheds leading 22-0.
The Tigers admirably fought their way back into the contest after the break with Blake Austin dummying his way over seven minutes into the second stanza, before Robbie Farah dummied his way over four minutes later to claw the score back to 22-12.
A Widdop penalty goal stiffened the Dragons and then they created space out wide for Morris to cross for the match-sealing try.
In an interview with Channel Nine, Potter said he was keen to stay on amid suggestions it was a case of him or club boss Grant Mayer who would exit.
- AAP