Mike Jones headed the Shakers into a 35th-minute lead before Brian Barry-Murphy coolly slotted home his first goal of the season just three minutes later.
Knill feared the worst as the mist grew denser at the Fraser Eagle Stadium but the Shakers managed to see out a thoroughly deserved victory, which takes them back up to sixth in League Two.
"I worried about the fog about three times," he said. "We had a white ball then an orange ball, then the white ball came back out.
"At 2-0, you do think, `here we go, it's going to be called off'. Thankfully the referee let the game continue and I would have been really disappointed had he not.
"That's nine points out of 12 this month and it puts us where we really want to be. The lads have been fantastic to turn things around after what was a poor month in October so full credit to them."
Credit
Bury keeper Wayne Brown certainly deserves credit as his third penalty save of the season prevented John Mullin pulling a goal back before half-time after Efe Sodje brought down Greg Blundell.
The Shakers were content to stand firm in the second half and Rostyn Griffiths' long-range effort was the best Accrington could muster until sub Jamie Clarke fired a 79th-minute spot-kick straight down the middle.
"The supporters were fantastic," said Knill. "When things weren't going for us they were behind the team.
"We defended solidly and had some pretty good finishing in the first half. After that you expect them to come at you - they're at home and they're 2-0 down.
"We changed the shape to a 4-5-1 and I thought it worked well. Some might say it was boring or negative but I think it was a pretty professional performance because it is a really tough place to come."
BURY: Brown 8; Scott 7, Sodje 6, Futcher 8, Buchanan 7; Bennett 7, Dawson 7, Barry-Murphy 8, Jones 7 (Howell 60, 7); Hurst 8 (Cresswell 60, 7), Bishop 7 (Morrell 88).
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