Knill's delight was obvious at the final whistle after defender Ryan Cresswell headed home the game's only goal in the 79th minute.
The Shakers had lost three games in a week ahead of the trip to Meadow Lane.
"I'm delighted to be back to winning ways," said Knill.
"We were a bit lucky at times, but that's been missing of late. We've done everything right but just not had that bit of luck.
"But we had some pretty good play as well. We just had to get back to playing like that because it had been a disappointing week.
"I don't think we deserved to lose at Bradford, but we did, so we've been on at the players all week about being committed to what we want to do and what we want to achieve.
"The most important thing was the three points. We had to stop the slide and it will keep all the doubters away because we haven't got a league game for two weeks now."
The Shakers dominated the first half, with Mike Jones missing an early chance before hitting a post, while recalled striker Andy Morrell fired narrowly wide.
Andy Bishop was denied just after the restart before Cresswell broke the deadlock from the impressive Jones' free-kick.
Bury then breathed a huge sigh of relief as Myles Weston's close-range effort went wide at the death.
BURY: Brown 7; Scott 7, Cresswell 7, Sodje 7, Buchanan 7; Jones 8, Dawson 7, Barry-Murphy 6, Bennett 8; Bishop 6 (O'Grady 77), Morrell 7 (Hurst 82). Subs: Haslam, Baker, Racchi.
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