The visitors have comfortably the strongest defence in the Championship but were surprisingly pummelled 3-0 just 20 or so miles down the road at Colchester seven days ago.
They were back to form here though, largely restricting Ipswich to long-range efforts as the Blues failed to click in attack, despite having plenty of possession throughout.
Stoke were little better with Mamady Sidibe and Ricardo Fuller largely kept at bay during a poor 90 minutes, but Lawrence's angled drive was enough for the points.
Fuller shot over inside the first 15 seconds after a long ball over the top, but that early promise soon fizzled out into a tame match at Portman Road.
Steve Simonsen made the first of several comfortable saves on nine minutes, gathering Dan Harding's poorly-hit 20-yarder before Owen Garvan curled a 25-yard free-kick not far wide.
Loanees Salif Diao and Lee Hendrie both went into the book as Ipswich enjoyed a decent spell of possession, frustrating the visitors, but they were able to do little with it. Carl Hoefkens volleyed over for Stoke, Darel Russell fired way over from 30 yards and Lewis Price comfortably gathered a low strike after a powerful run from Sidibe.
Fuller curled an effort wide against an Ipswich side where he spent a short loan spell last term before Alan Lee drew a decent diving save out of Simonsen after Gary Roberts blocked a Hoefkens pass.
Fuller shot into the side-netting from a Russell pass at the end of a neat move, and then Simonsen saved easily from Jon Macken and Sylvain Legwinski efforts.
Stoke made a fast start to the second half, and Russell forced a save out of Price inside 40 seconds before Richard Naylor got back to clear a looping Sidibe header which was on its way in after he outjumped Price to reach Clint Hill's deep cross.
Price saved an angled Fuller attempt before two good chances for Town loanee Macken, whose touch deserted him first on a good Gavin Williams pass before shooting into the side-netting from another Williams ball.
Stoke netted what proved to be the winner in a breakaway move with 19 minutes to go. Hendrie shaped to shoot but back-heeled the ball into the path of Lawrence whose low angled drive beat the diving Price, who may feel he could have done better.
Town tried to press for an equaliser, but rarely threatened, despite throwing centre half Jason De Vos forward late on with Garvan, Williams and Macken all off target from 20 yards, as the visitors held on comfortably.