That victory made it four wins in a row for Glasgow in the inter-city derby but Evans insists he and his team-mates will still be going hell for leather for the full 80 minutes to try and make it a full house.
"We have to lift the aggression even more in the next game," Evans told The Scotsman, after Glasgow overturned a half-time deficit to run out comfortable victors in part one of festive fixtures.
"The main word we used going into the game at Firhill was 'relentless' and that's what we have to continue doing over the next few days and into the next game."
Edinburgh have lost just once at home in the Magners League this season, recording four straight wins over Leinster, Ulster, Treviso and Connacht since a narrow opening day reverse to Munster.
But Evans is confident that Glasgow can match last season's Murrayfield triumph if the Warriors cut out their own mistakes and improve their discipline.
"What we said in the changing room after the game was that there was not much to fear from their side. It's about sorting ourselves out," added Evans.
"We gave them a lot of ball - all of their points came through penalties. Apart from one good set play they did from a centre scrum, they never really looked like they were going to score a try.
"I always thought if we could get some position in their half we could do some damage and come away with points, but when they were in our half it was a similar thing as we kept giving away penalties."
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