Dyer converted a counter-attack 17 minutes from time, ramming home a cross by Tom Cleverley.
MK Dons ended a run of four games without a win, to stay a point ahead of the Iron. They were 5-3 victors at Cheltenham Town.
Even a hat-trick from transfer-listed striker Damian Spencer could not lift the Robins, who are without a win in nine league and cup matches and sank to the bottom of the table.
The Dons striker Aaron Wilbraham scored a hat-trick and winger Jemal Johnson scored twice as the visitors built up a 5-1 lead before a late Cheltenham revival.
Although the top two teams won, most of the teams immediately around and below Scunthorpe dropped points, with Peterborough losing 1-0 at Huddersfield Town.
Michael Collins goal sealed all three points for the Terriers. The Posh had started the day in third, but drop below Scunthorpe to fourth after the defeat.
The Swindon Town goalkeeper Petr Brezovan took a starring role as Oldham Athletic were held to a goalless draw at Boundary Park. The Latics remain in sixth place, the final play-off position.
Leeds United could not take advantage of the slips, as they lost 1-0 at Walsall to remain four points adrift of the play-offs. Troy Deeney scored the goal.
Brighton & Hove Albion's new signings made an instant impact as they ended a run of four straight home defeats with a 2-1 success over Hartlepool United.
Calvin Andrew headed home a 90th minute winner after fellow capture Seb Carole came off the bench to set up Nicky Forster's second-half equaliser.
Dougie Freedman ended Southend United's miserable league run, with his second-half header sealing a 1-0 home win over Bristol Rovers.
Colchester United extended their unbeaten run to nine games with a 2-0 success at Carlisle United, with David Perkins' strike adding to an early own goal from Danny Livesy.
A header from the Yeovil Town substitute Gavin Tomlin deep into stoppage time gave the Glovers a 1-0 win at Leyton Orient.
Stockport County eased to a 4-1 home win over Hereford United, with the tone set when Dominic Blizzard put them ahead just 13 seconds into the game.
Mark Carrington and Joel Grant fired in late goals as Crewe Alexandra stunned Tranmere Rovers with a late fightback to win 2-1 at Gresty Road.