It was the biggest win of the season for the home side, who stretched their unbeaten run to 16 games.
They needed just five minutes to open the scoring from the second corner of the game. Portsmouth could only half clear it and, when the ball came back in to the box, Syers found room to get in a left-foot shot that took a deflection to beat goalkeeper Trevor Carson.
Leading marksman Sam Winnall made it 2-0 with his 17th goal of the season in the 36th minute as he finished clinically into the bottom corner of the net after a clever flick by Gary McSheffrey put him free in the box.
Scunthorpe struck again before the break with Syers netting his second goal of the game, tucking in a left-foot shot on the turn after some great work by striker Paddy Madden.
Pompey, beaten only once in their previous five away games, had little to offer in reply, with nothing on target to trouble home keeper Sam Slocombe.
The visitors made a double substitution at half-time, but it was Scunthorpe who struck again three minutes after the interval as Madden netted his first goal for the club after a header from centre-back David Mirfin had been well blocked away by Carson.
The Iron added another before the hour when Syers completed his hat-trick with a simple tap home after a flowing move which ripped apart the Portsmouth defence.
Only a good save by Carson prevented Paul Hayes adding a sixth late in the game before fellow substitute Michael Drennan headed home an 85th-minute consolation for Pompey with their first effort on target.