Syers, who helped Doncaster Rovers win promotion to the Championship last season, struck twice either side of half-time as the Iron came from behind to halt a barren five-match run.
Scunthorpe, who sacked manager Brian Laws after the midweek 2-1 FA Cup defeat by Grimsby Town, spurned several good chances before Tom Craddock headed Portsmouth into a 36th-minute lead.
Pompey's first flowing move of the match culminated with Craddock heading his maiden Blues goal from a Ricky Holmes cross.
Portsmouth's lead lasted only four minutes, though, with Syers equalising at the far post after Andy Dawson's corner found its way through the six-yard box.
Deon Burton was the culprit as Scunthorpe bungled more chances before Syers grabbed their winner - Trevor Carson spilling Sam Winnall's left-foot shot into his path.
Portsmouth twice hit the Scunthorpe woodwork but Carson twice made fine saves to deny the visitors.