Cardiff had arrived at Molineux on the back of a run of six defeats in seven games that had seen them collect just one point from 21.
It had put Lawrence's position under the microscope but his players responded superbly to stun a Wolves side who are still searching for their first home win of the campaign.
Paul Parry fired Cardiff ahead only for Carl Cort to equalise 60 seconds later.
But two goals in the space of 11 second-half minutes from Peter Thorne and Kavanagh secured Cardiff's badly needed win.
A late strike from Wolves' skipper Paul Ince proved to be no more than consolation for Dave Jones' side.
Wolves had gone into the game seeking a third successive league win after back to back away victories at Brighton and Plymouth.
But they had no answer to Cardiff's impressive start to the second half as they continue to struggle to force their into the leading pack and they left the pitch with the boos of their fans ringing in their ears.
Wolves were stunned after 11 minutes when Parry was picked out by a cross field ball from Jobi McAnuff before seeing his shot deflected past Jones off Wolves' debutant right-back, Keith Lowe to hand Cardiff the lead.
But Cardiff barely had time to celebrate only their second goal in five games before Wolves were back on level terms.
Ince sent Seol Ki-Hyeon clear and the South Korean international whipped in a left-wing cross that Cort instinctively met the centre with a first-time shot for his second goal of the season.
Cardiff were then indebted to their goalkeeper Tony Warner who pulled off a stunning one handed save to push away a header from Seyi Olofinjana on the stroke of half-time to keep them on level terms.
It proved to be an escape that Cardiff took full advantage of. Thorne, who had opened his account for the season with a double in the midweek Carling Cup win over Milton Keynes, rose at the far post in the 48th minute to head home a Parry cross.
Wolves fate was then sealed after 59 minutes with Kavanagh's wonder strike.
Goalkeeper Jones could only punch a corner from McAnuff into the path of Kavanagh whose first-time right-foot volley dipped over Jones and into the roof of the net.
Wolves mounted a late rally when Ince headed home Ki-Hyeon's corner, but Cardiff were able to hold on for their priceless success.