There was nothing the U's goalkeeper could do about the opener though, as Murray turned home Nicky Wroe's shot at the second attempt in the sixth minute.
Two further chances fell the way of the Colchester striker shortly after, but Carroll saved again from the first attempt before Ibehre headed wide when he should have guided his effort on target.
Nonetheless, the visitors continued to come forward and Marcus Bean's free header from six yards bounced over the frame of the goal.
Carroll was kept incredibly busy throughout the first half as he then deflected Ibehre's shot away with his leg to ensure the home side went into the break leading.
The home side almost grabbed a goal early in the second period too, but Colchester's Tom Eastman was relieved to see his sliced, hurried clearance spin just wide of the post.
Carroll continued to perform heroics as he denied Freddie Sears after an hour in a one-on-one situation, but Sears eventually got the better of the 36-year-old when he raced clear and calmly slotted the ball underneath his adversary.
However, Notts regained the lead just two minutes later through Noble, who curled an effort into the back of the net.
With 13 minutes left, Cieron Keane was shown his second yellow card of the evening, but Mustapha Dumbuya and Hayden Mullins still had time to spurn late chances before Wroe was shown a second yellow card in injury time as a depleted Notts side held on to secure their first win of the 2014-15 campaign.