The Scots had trailed after just 90 seconds when a floated pass by Dan Parks took a crooked bounce and sailed over the head of hooker Lawson.
Alert winger Cristian Savan scooped up the loose ball and was left with a clear path to the line from 35 metres. The easy conversion was added by full-back Danup Dumbrava.
Dumbrava was quickly back in the spotlight when he sent over a long-range penalty.
The Scots found their rhythm and, following a near-miss by Brown, lock Scott Murray battled his way through, with Chris Paterson's kick reducing the gap to three.
Romania suffered a further double setback when prop Cesar Popescu was yellow-carded.
Then, within a minute, the visitors had bagged their second touchdown through centre Andy Henderson.
Paterson sent over the conversion from a wide angle to put Scotland in the driving seat, and he made the picture even brighter by scoring a superb try just before the interval.
Craig Hamilton inflicted the initial damage before Bruce Douglas delivered the telling, final pass to the unmarked Paterson.
With the last kick of the half, Dumbrava revived the Romanian hopes by confidently slotting his second penalty.
But Paterson replied in identical fashion just after the restart to restore the eight-point margin.
As both teams grew careless, the penalty ping-pong continued with Dumbrava completing his penalty treble from point-blank range.
Scotland stepped up the pace again and Lawson's moment of magic arrived when he marked his maiden cap with a try, burrowing over in the wake of tight pack work.
Romania refused to buckle and stayed in the hunt thanks to another Dumbrava strike.
But any prospect of a meaningful fightback ended when Parks snatched Scotland's fifth touchdown, pouncing on poor home defence behind their own line. Paterson added the goal.
There was still time for Brown to snap up his debut score in the closing stages.
Story taken from Sporting Life (who seemed to think Gordon Ross is Scott Lawson!)