Warriors hold a 23-14 aggregate lead from the first leg, the victory taking them back to fourth place in the PRO12 table.
But the talismanic Glasgow skipper has no doubt Edinburgh will come out with all guns blazing.
And Kellock believes a solid start will be pivotal to Glasgow's hopes of securing their first double over Edinburgh in three campaigns.
He said: "We know Edinburgh will be like a wounded animal. Their pride is on the line, this is on their turf and in front of their fans, and they will be determined to come out on top.
"I think we can expect them to throw everything at us early doors and it will be vital we come out and try and repeat the way we started in the first leg. But it would be fantastic to record our first win in the capital in three years, and that is what we will be trying to achieve.
"It is going to take a massive effort, but after the way we played in the opening game, we will be heading East full of belief and confidence."
Head coach Gregor Townsend is sure to remain loyal to the Ruaridh Jackson and Niko Matawalu half-back partnership that wreaked havoc on Michael Bradley's men last week, and Kellock was saluted the Warriors backline.
The Glasgow skipper said: "What really pleased me as a forward was the way our backs really scanned the Edinburgh defence and took the right option.
"Both Ruaridh and Niko had great games and DTH Van Der Merwe demonstrated just what a great finisher he is with his two tries.
"We were very clinical in how we played and, when we get opportunities on Saturday, we must repeat that. But looking back at the first game I just felt we controlled proceedings very well.
"We knew Edinburgh would come back at us after the interval and they certainly did that, but we held firm and weathered that storm and ultimately it was us who were pushing for the bonus point try at the death. But we are under no illusions as to how tough it is going to be."
With last Friday's victory ending a four-game losing streak in domestic and European competition and restoring Glasgow to the play-off positions for the first time in a month, a second success over the men from the East would give Warriors a huge platform into the second half of the season.
Kellock added: "These games are always huge in that if you can come out on top they just give you such a boost for the rest of the season.
"We have Treviso coming to Scotstoun a week on Friday and it would be great to be going into that on the back of a double over Edinburgh.
"But we know there are still things we can improve on from the first leg – and know we will need to as Edinburgh will lift their performance level."