"I was feeling a little bit of pressure coming in as defending champion. I had a lot of people coming to support me, and I wanted to get off to a good start," he said.
"But I feel really good, I feel everything's there in front of me. I know what I'm doing, there's nothing in the back of my head concerning technique, so it's good to be feeling like that."
Davis, who beat namesake Steve to qualify for Glasgow, admitted he feared the worse when Fu fought back from 2-0 down.
"To be 2-2 was devasting really," he said. "It was better after the interval but I'm pleased to get over the line. I was glad to knock those last few balls in but the yellow was difficult.
"It was game ball, if I missed it it could have been game over but if I played it nicely I'd be on the green. Early on in the last frame I had a couple of bashes and got lucky."
In the evening session, England's Joe Perry beat Marcus Campbell of Scotland 5-2, before Ireland's Ken Doherty saw off Englishman Mark Selby 5-3 in the remaining match.
Video - Davis comes through safety battle (UK users only)
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