The former Sunderland winger produced the one moment of true quality in a battle of a game as Tony Pulis' men, who have suffered just one defeat in their last 18 league outings, claimed a fifth successive victory.
The opening 20 minutes were incredibly tight, with both sides maintaining a very high work-rate.
Rory Delap finally forced a save out of Stephen Bywater in the 21st minute before Ipswich carved the first real chance a minute later.
Jon Walters knocked the ball down to strike partner Alan Lee, who should have done better than balloon his eight-yard shot over the top.
But Stoke began to up the ante as Glenn Whelan's shot stung Bywater's fingers and Ricardo Fuller hooked a long-range attempt narrowly wide.
And the deadlock was broken with a quite outstanding goal by Lawrence three minutes before the interval.
Fuller was blocked off as he attempted to reach Mamady Sidibe's flicked header, but the loose ball ran to Lawrence who drove in an unstoppable rising shot from 25 yards.
Jim Magilton made a change at half-time with Danny Haynes replacing Alan Quinn and Ipswich started the second period with more of a spring in their step.
But Magilton was in hot water with the officials in the 58th minute when he was sent to the stands after a heated discussion with referee Mike Jones.
Stoke regained the initiative with Sidibe going close twice, the first with an overhead kick from Lawrence's delivery to send the ball bouncing a foot wide.
But the visitors were still in with a shout and Steve Simonsen, now under serious pressure from new loan signing Marton Fulop, made an excellent diving stop from Velice Sumulikoski.
Stoke played out the closing stages in some comfort, however, to retain a one-point lead at the top ahead of Bristol City.