The midfielder chose the perfect moment to end his goal drought since a summer switch from Glanford Park, producing a stunning diving header just after the hour mark as Town made it two wins from three under their new manager Lee Clark.
Goodwin delivered a tough-tackling display against his former employers and his goal after 65 minutes was enough to destroy the Iron's six-match unbeaten run.
Town had a couple of good early chances but Keigan Parker's powerful shot was deflected away by Sam Togwell. From the resulting Gary Roberts corner, Nathan Clarke sent a thumping header goalwards only for it to be blocked by Togwell.
Phil Jevons ghosted in for another great chance but lifted his finish over the bar before Ben May headed over for the Iron and also had an effort ruled out for offside.
Town took control after the break but Parker was again off target before he set up Roberts only for the 'goal' to be ruled out.
Parker then shot straight at keeper Joe Murphy and Gary Hooper was denied by Alex Smithies.
But just as it was beginning to look as if it wasn't going to be Town's day, it was the unlikely goalscorer Goodwin that broke the deadlock from Roberts' corner.
The home side survived a few scares after that and Scunthorpe ended with 10 men after substitute Ian Morris was carried off late on with all replacements used.
Scunthorpe piled forward in the allocated five minutes of stoppage time but were caught when Danny Cadamarteri latched onto a clearance and went down under challenge from Andrew Wright.
Roberts was left to race through and slot into an empty net for his eighth of the season with the final kick ogf the match.