County named an unchanged side to the team that faced Cambridge United on Saturday, with just a change on the bench, as Jazzi Barnum-Bobb replaced Jordan Green.
The hosts were also unchanged and fielded hot-prospect Omar Bogle, who has netted on eight occasions so far this season, including a hat-trick against Stevenage in last August.
County looked to test Grimsby 'keeper James McKeown early on and Mark Randall made sure the shot-stopper was alert when his early free-kick from the left had to be claimed underneath the crossbar, at was an awkward height from the 'keeper.
Grego-Cox looked to stretch the hosts down the right and it was his cross that provided Jon Parkin with the chance to head a well-directed cross just past the right-hand post after Grego-Cox was able to beat his man out wide.
Grimsby had the best chance of the half when Danny Andrew cross managed to find its way to the lurking Kayden Jackson, who mistimed his close-range effort and the ball bounced harmlessly wide of the County goal.
Joe Day looked alert in the County goal and was on hand to tip a Dominic Vose effort past the post that looked like it may have been curling onto target from just outside the area.
The hosts managed to win eight corners during the first half, but the County defence looked structured and was able to deal the threats from wide.
Into the second half and County enjoy a good spell of pressure, with Ben Tozer looking to utilise his dangerous long-throw to cause the home side problems.
Jon Parkin saw a thumping header cleared off the line by a stray boot of Luke Summerfield early in the final forty-five minutes, after 'keeper McKeown looked to have been beaten and County continued to amount chances on the Grimsby goal.
As he did in the first-half, Joe Day produced another fine reaction save to deny Omar Bogle, as the forward stabbed and effort goalwards from close-range and out of nowhere Joe was there to tip the ball around the post.
Jon Parkin again caused problems inside the area as the striker was able to latch onto a corner from the left and flick a header towards goal that saved well by McKeown, who saw the ball late in its flight.
In the final moments of the game Bolarinwa was brought down in the area by Dan Butler and the referee pointed straight to the spot. Omar Bogle confidently stepped up and dispatched the penalty to give the hosts a late winner.
FULL TIME: GRIMSBY TOWN 1 - 0 NEWPORT COUNTY AFC
NEWPORT COUNTY AFC: Day, Butler, Bignot, Bennett (c), Cameron, Randall, Tozer, Rigg, Grego-Cox, Parkin, Healey (Jackson 67')
SUBS: Bittner, Jackson, Jones, Barnum-Bobb, Sheehan, Myrie-Williams, Compton
BOOKINGS: Scot Bennett, Jon Parkin
REFEREE: Ben Toner
ATTENDANCE: 4296 (39)