First-half tries from Sean Maitland and fly-half Ruaridh Jackson put the Warriors in charge before Henry Pyrgos touched down in the 53rd minute.
The Warriors survived a late fightback from Edinburgh, with Roddy Grant and Tim Visser going over to ensure a tense finish.
Scotland face England in their Six Nations opener in just over four weeks and with Johnson watching in the stands, Kellock and co made a fine claim for inclusion.
"We don't need any motivation for matches like these. Our boys did themselves a lot of good and Scott will have been watching that," Kellock told the Scottish Daily Record.
"It was an outstanding effort by us. The energy in the Warriors dressing room is phenomenal at the moment - from one to 15.
"There probably were not too many individual stand-outs and that was because everyone was exceptional.
"Take the back row for example - Ryan Wilson and Bobby Harley again battled superbly and showed consistency is what it's all about.
"Henry Pyrgos made a huge impact at scrum-half and so did Duncan Weir when he came off the bench. Up front, Moray Low had a point to prove and did that.
"Our scrum was very dominant. Chunk [Allan Jacobsen] has always been a great scrummager for
Edinburgh and Moray should now enjoy what he achieved against him and continue to work hard.
"We know how good he is when he gets it right."
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