The result hinged on the sin-binning midway through the second half of Paul Davidson for a late tackle on Tony Smith.
Phil Jones' penalty cut Saints' lead to two points and the feeling that neither side could afford to be short-handed in a game like this intensified.
Mark Reber, later to go off with a suspected broken arm, put Saints under pressure with a clever kick. From the resulting possession, Smith's equally slick pass sent Simon Haughton striding over.
Four minutes from time, a flash of vintage Gary Connolly made the game relatively safe.
"I'll take that one. That will do for us," said Goodway as his team closed the gap on Bradford at the top of Super League.
Although this was a fluctuating affair, Wigan, after so much trauma during the week, showed the potential to win it from the start.
Their fans have been waiting for a spark of creativity from half-back in recent weeks. Smith and Greg Florimo, both under pressure to produce for their new coach, did just that after 10 minutes, engineering a huge gap to send Neil Cowie through.
The prop resisted the temptation to try to go all the way himself, instead presenting the try to the supporting Kris Radlinski.
Jones' conversion, plus a penalty after Chris Joynt had been whistled up for interfering at the play-the-ball, gave Wigan a handy lead, but one that disappeared without trace in a couple of minutes of carelessness.
First Tommy Martyn, who had earlier gone close to a try from a Sean Long kick, followed his own toe-poke to capitalise on the failure of Radlinksi and Mick Cassidy to clear.
Then Jones' fumble from Martyn's high kick yielded a St Helens scrum, from which Martyn's back flick sent Paul Newlove crashing over. Long's two conversions gave Saints a four point advantage.
Five minutes from the break, a breathless match lurched the other way once more. Fereti Tuilagi's tackle seemed to have ended the danger when he stopped Haughton, but Wigan moved the ball quickly to the right where Connolly's break released Jason Robinson to touch down in the corner.
Jones' cool conversion from the touchline gave Wigan their two point lead at the break.
Long squared it up with a penalty and, with Saints dominating the early stages of the second half, it was no shock when Kieron Cunningham muscled his way over from dummy-half. Joynt came desperately close to a try that could have clinched it, but Wigan showed tremendous resilience, just as Saints will now have to do, with two defeats on the trot and their next game at Bradford on Friday.
"It wasn't a case of one player's sin-binning costing us the game," insisted their coach, Ellery Hanley. "We had the opportunities to win the match, but we didn't take them."
St Helens: Atcheson; C Smith, Tuilagi, Newlove, Stewart; Martyn, Long; O'Neill, Cunningham, Davidson, Jonkers, Perelini, Joynt. Substitutes used: Sullivan, Matautia.
Wigan Warriors: Radlinski; Robinson, Moore, Connolly, Jones; Florimo, T Smith; Cowie, Clarke, O'Connor, Betts, Cassidy, Gilmour. Substitutes used: Mestrov, Reber, A Johnson, Haughton.
Referee: S Presley (Castleford).Reuse content