The winger struck 15 minutes from time to break Blackburn's brave resistance and leave Sam Allardyce's side with much work still to do.
Stoke almost got off to the best possible start when Glenn Whelan's volley was deflected over the bar by his team-mate James Beattie.
But Rovers successfully negotiated the early pressure and began to take charge as Morten Gamst Pedersen fired too high and Keith Andrews shot wide.
The pace of a highly-charged contest was frenetic and there were several meaty challenges before Stoke's Andy Wilkinson was booked for flattening El Hadji Diouf.
City's Ryan Shawcross was then lectured by referee Howard Webb after tempers became heated during an untidy wrestling match with Chris Samba.
A bruising encounter was certainly earning no points for its aesthetic qualities as Pedersen came close to matching Rory Delap's prowess in the long throw department.
And not many fans in another Britannia Stadium full house could have been too disappointed when Mr Webb brought a scrappy first half to a close.
There was more of the same at the start of the second period, with Samba and Ryan Nelsen forced to perform heroics as they defended more Delap throw-ins.
It really was untidy stuff as Stoke's Ricardo Fuller and Blackburn's Stephen Warnock were cautioned for fouls on Samba and Whelan respectively.
But Stoke finally began to turn the screw with Lawrence providing some desperately needed inspiration from the right flank.
The winger's venomous shot brought the game's save of note in the 55th minute as Paul Robinson arched backwards to tip the ball over the top.
And Lawrence delivered an excellent cross less than a minute later when Matty Etherington should have broken the stalemate.
Etherington steamed in unmarked at the far post, but steered his header wide from six yards.
Lawrence was not to be denied, however, as he did land what proved to be the decisive blow that sent 24,000 home fans delirious.
Danny Higginbotham's cross was headed on by Beattie to leave Lawrence one-on-one with Gael Givet at the far post.
Lawrence didn't connect properly with his shot after wriggling free of Givet's attentions, but the ball just had enough steam to roll over the line after striking Robinson's body.