The Greens struggled to get anything going in the first half having made a number of changes to their starting line-up. As a result Greg Ponton's three penalties kept Kelso in with a chance in the pool G match.
However, in the second half Hawick got into their stride to overpower the visitors. Tries from the home side came from Garry Johnstone, David Lowrie, Craig Charters, Nick MacTaggart, Craig Robertson, Sean Linton and Steven Anderson.
Meanwhile, Whitecraigs coach John Shaw saluted his players efforts after they pushed top flight West of Scotland hard in their pool I match at West Lodge.
With Whitecraigs currently top of Premier Three this one was always going to be tough for West and so it proved with a late try by Mark Davis needed to seal a 15-5 win.
Shaw, who had seen his side take a 5-3 lead in the first half through an Ian Laidlaw try, said: "I was proud of the players' efforts as they worked hard against West and dominated in the scrums. It was just disappointing that we couldn't see the game through, but in the end missing four or five regular players hurt us. Nevertheless the experience will have been good ahead of some key league fixtures coming up."
Other lower league sides who pushed Premier One clubs hard were Dumfries and Dalziel.
Premier Three side Dumfries went behind to Glasgow Hawks after tries by Ross Miller, Grant Strang and Craig Gossman, but fought back with a Sam Hiddleston hat-trick. Eventually tries from Kerr Gossman and former Scotland under-20 scrum-half Kris Hamilton saw Hawks home 29-21 at New Abbey Road. In Motherwell Boroughmuir scraped to a 10-0 win over Dalziel thanks to a try from Jamie Doubleday and a penalty and conversion by teenager Harry Leonard. Captain Craig Simmonds and Fraser Stangoe impressed for the hosts.
Dundee HSFP blew Musselburgh away in the first 40 minutes to win their pool D clash. The Mayfield men led 45-3 at half-time in East Lothian with in-form winger Stewart Coleman notching three tries in the first 20 minutes. In the end the final score was 50-3.
Holders Ayr eased through 57-10 at Perthshire, while Premier One leaders Melrose chalked up a 34-10 win at Ardrossan Accies' Memorial Field.
Scotland club internationalists Fraser Thomson and Callum Anderson both scored two tries for Melrose with Bruce Colvin and Nick Beavon also scoring tries.
Another Borders side, Selkirk, were in good form in Dundee. They warmed up for their Premier B battles in the weeks to come with a 57-5 win over Morgan Academy.Nine tries were scored by Fraser Harness' men with Conor Paton and teenager Nyle Godsmark grabbing two tries each. Nyle's brother Ryan was also among the try scorers as was Mike Rutherford.
Stirling County were clinical in seeing off Premier B rivals Peebles 31-0 at Bridgehaugh in pool H. Craig Black, Graham Gilliland and Ben Addison scored the host's tries.
Watsonians saw off Kirkcaldy 46-19 at Myreside, Aberdeen Grammar had to fight hard to oust Howe of Fife 30-24 at Rubislaw and Stewart's Melville edged out Hillhead/Jordanhill 18-13 at Inverleith.
Edinburgh Accies got the better of Jed-Forest 25-15 in pool D, Heriot's were clinical in winning 29-8 at Cartha Queens Park, GHA defeated Dunfermline 30-17, Biggar saw off Haddington 32-10 and Gala edged out Falkirk 14-10.
The clash between Hamilton and Currie was postponed.