Murray's superb seventh-minute strike gave County the perfect start before Hollis then headed in his third goal in three games to double their lead.
County had chances to extend their advantage after the break but with other results going their way, Shaun Derry's side still climbed out of the drop zone.
The Magpies started ferociously and were rewarded when Murray broke clear to slide a super finish beyond U's goalkeeper Sam Walker.
But the visitors fought back and were unfortunate not to level when Freddie Sears' shot hit the post and County goalkeeper Bartosz Bialkowski then pushed a shot from Alex Gilbey round the post.
But as the anxiety grew inside Meadow Lane, the Magpies gave their fans some relief just before half-time, Hollis heading in from Alan Sheehan's free-kick.
Derry's side continued where they left off after the break with Murray close to grabbing his second with a terrific volley.
Jimmy Spencer also went close, but County were not made to pay for their wastefulness as they coasted to three vital points.