Both sides had endured a tough fortnight in the Heineken Cup with successive defeats but while the Gunners have struggled in the RaboDirect PRO12 as well, the free-scoring Scarlets are one of the early pacesetters.
And despite a 23-point haul from Edinburgh fly-half Harry Leonard, four first-half tries from the Welsh region, including a double from George North, proved vital.
And former Wales international winger Jones admitted that his side came into the clash knowing that a victory could make all the difference in getting their campaign back on track.
"We should not underestimate how important a match this was in the context of the Scarlets season," he said.
"It was a tough and hard-fought game and one we are pleased to win; particularly as this is a tough place to go and historically we haven't always performed away in Scotland.
"After a tough fortnight, the boys really showed their commitment and determination and their mental strength to come away and get a win tonight.
"Edinburgh were hurting after their poor European results so we knew we could expect a lot of intensity and intent from the home side.
"Our focus was to get to back on track and back up our results so far this season in the league and it is a big boost for us after the disappointment of the last fortnight.
"I am very proud of the boys' determination and spirit tonight; we've talked about closing out games and particularly being able to finish teams off as we did under pressure tonight. This is probably a very significant result away from home.
"We look forward to our home game against Zebre next Saturday and hopefully continuing a strong run in the RaboDirect PRO12."
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