Billy Jones first gave them the lead with a goal on his debut, firing in a low drive into the bottom corner from Conor Washington's cross.
The Exiles looked to be in control but a quick counter-attack from the visitors ended with Tom Naylor turning the ball into his own net.
Robbie Willmott edged the hosts back in front but things went from bad to worse in the second half for Naylor. He scored his second own goal of the game before conceding a penalty for a foul on Kevin Ellison that Padraig Amond converted for the win.
It's was the Shrimps' fourth successive win in Sky Bet League Two despite Bentley admitting they have not been at their best this season.
Bentley said: "It's a great win for us.
"The fans certainly get behind the team at Newport and make it difficult for the opposition.
"They came out of the traps really quickly in the first half and I thought we were lucky to concede just two because it could have been more.
"But we addressed a few things at half-time and bucked our ideas up in the second half and caused them problems.
"On another day it could have been 8-8 but luckily for us we got the third goal and the win.
"We haven't been at our best in the league all season but we've got an unbelievable desire and spirit to win football games and that's what we are doing at the moment.
"As a manager you are always looking for a little bit more, you want your side to be a bit better on the eye but that's not always the case.
"We are doing the ugly things very well and hopefully as the season goes on we will be able to put in some good performances to go along with that."