Director of Rugby Phil Davies praised his side on the night for playing in the right areas at the right time to claim a vital win in Pool 2.
And Williams knows the Blues will need to reproduce that at the Scotstoun Stadium against fired-up Warriors who will be keen for revenge.
"We had that balance to our play and we need to repeat that, go up there and back it up," he said.
"I felt Patch (Rhys Patchell) and myself played in the right areas at the right time. We went from deep when it was on.
"My opposite number, Nikola Matawalu, is a great player for Glasgow. We looked at him in the week ahead of the game and they clearly wanted front foot ball. But all credit to Macauley Cook and Rory Watts-Jones as they slowed it down.
"We can take confidence from last week. They came at us all guns blazing and the fact we won gives us confidence we can do a job up north.
"However, it will take a lot of hard work. They (Glasgow) have proved they are a top side in the league and Europe so we need to be at our very best."
Williams was also pleased that Blues backed up the performance against champions Toulon in the previous round.
But he acknowledged the focus was now firmly on Friday night and striving to claim another win to keep qualification hopes alive from the pool stages.
He added: "For a lot of us involved in Toulon game it was a chance to back that result up. A lot of people said it was one off and we wanted to prove that wasn't the case. I felt we answered a few critics. Across the field, from 1 to 23, it was a fantastic performance.
"We now go to Glasgow and it would be naive to think they will play the same. They will change things up and will target different areas.
"We will also change things, look to stay fresh and on top of our toes. It is an exciting game and if we can win it will open things up and be great for our campaign.
"If we get the right result Friday night it will help our RaboDirect PRO12 form, it has a knock-on impact and hopefully we can then go into Christmas on top form."