The result ended a sequence of three straight five-point league wins for Biggar, who conceded the opening try within the first five minutes.
This was scored by winger Matthew Smith who came onto a good line from some five metres out, wrong footing the Biggar defence.
Converted by Andy Bell, Lasswade were 7-0 ahead.
Biggar were finding it tricky playing into the wind but the hosts got back into it when Jamie Orr burst clear to cross from some 40 metres out and by beating the cover defence on the way.
Kicking into the strong breeze was always going to be tricky in the conditions and so it proved as Carne Green was off target with his conversion attempt and then again some 10 minutes later when the ball rebounded out off the upright.
Lasswade then had one of their number sin-binned for failing to retreat at a Biggar penalty which Green ran but Biggar were thwarted by a strong defence.
And Lasswade then went 14-5 ahead by half-time when hooker Darren Tiffney crashed over for a try which was converted by Bell.
Biggar hit back early in the second half when Reive fed Green who popped the ball inside to Stewart who crossed for the try.
The scorer had earlier come on for Jamie Orr who sustained a shoulder injury.
Green’s conversion attempt was wide but at 14-10 Biggar were back in the mix.
And there was soon just one point in it when Green kicked a penalty which saw Lasswade’s Mark Wilson sin-binned for preventing fair release.
But the visitors clinched it with a late try by Wilson who sprinted over the line.
Biggar continue their league campaign this Saturday when they journey to Fife and league leaders Kirkcaldy, kick-off 3pm.