Stoke came back from two goals down to win and move top of the Championship.
Stoke's Lawrence scored twice, including the winner
Martin Paterson opened the scoring for Scunthorpe, volleying home Matthew Sparrow's cross on only seven minutes.
Jack Hobbs then headed Ian Morris' cross past Steve Simonsen to make it 2-0 before Liam Lawrence pulled one back for Stoke just after the break.
Richard Cresswell then volleyed Ricardo Fuller's cross into the back of the net to level before Lawrence grabbed his second to secure victory for Stoke.
Stoke manager Tony Pulis:
"We gave away two soft goals in the first half but the spirit of these players is never in question.
"There were no cups of tea thrown at half-time, but we had a good chat. The first 25 minutes we produced in the second half was fantastic.
"It's vital we win these sort of games because last season we slipped up."
Scunthorpe manager Nigel Adkins
"I'm feeling it (the pressure) and I'm really down at the moment. But I will get myself back up for Tuesday's game at Wolves.
"Nobody gave us a chance coming here but the players were superb in the first half. Everyone thought we would get a good hiding but that didn't happen.
"There are a lot of positives from that, but all the three goals we conceded in the second half could have been avoided.
"But I'm very proud of the players and our destiny remains in our own hands."
Stoke: Simonsen, Griffin, Shawcross, Cort, Pugh, Lawrence, Diao (Cresswell 54), Whelan, Delap, Sidibe, Fuller (Zakuani 90).
Subs Not Used: Hoult, Parkin, Gallagher.
Goals: Lawrence 53, Cresswell 63, Lawrence 67.
Scunthorpe: Murphy, Butler, Hobbs, Crosby, Williams, Sparrow (May 90), Goodwin, Cork, Morris (Forte 83), Horsfield (Hayes 51), Paterson.
Subs Not Used: Lillis, Iriekpen.
Booked: Butler, Goodwin.
Goals: Paterson 7, Hobbs 23.
Ref: Graham Laws (Tyne & Wear).