Despite playing into wind after the half-time break, Kelso scored 22 unanswered points to make it two wins from two in the National League.
Kelso opened their account on seven minutes with an outstanding try by their backs to put Corey Venus in.
Ben Cooper increased the lead with a penalty, but poor tackling allowed Biggar centre Mark Bertram to waltz over and Craig Parker added a penalty to level the scores at the interval.
Biggar had a try disallowed at the start of the second half, but Kelso weathered the storm and their forwards became moreinfluential.
Tries from Richard Minto and Michael Robertson made the game safe at 22-10.
Then, a deceptive turn of pace by Donald Seed set up Don Buckley for the bonus point try and Kelso still had time to add a fifth as Gregor Millar went over.
Kelso were also boosted by the return of Gareth Riddell after a long lay-off.