It had looked like Ivan Toney, who spent the first half of the campaign on loan at Wigan before being recalled by parent club Newcastle and sent back out to Scunthorpe, had won it for the visitors with a clinical finish eight minutes into the second half.
But Roberts had other ideas, with a cool finish from close range shortly after coming on to the pitch. Wigan had earlier twice led in a very entertaining first half containing four goals.
First Chey Dunkley headed home Max Power’s corner after only 13 minutes, before Tom Hopper equalised three minutes later at the third attempt after being denied by goalkeeper Christian Walton and then hitting the post with the rebound.
Will Grigg put Wigan back in front with a scruffy goal two minutes before the break but, in first half stoppage-time, Hopper added his second with a fine header into the corner of the net.
Preston are reportedly weighing up whether or not to make a fourth offer for Peterborough United left-back Andrew Hughes.
James Maddison has completed his move from Norwich City to Leicester City for an undisclosed fee.