Back at the club he led to promotion in 2003, Newell's organised and efficient side progressed with first-half goals from Peter Sweeney and Adam Proudlock.
And while the Mariners struggle in League Two, Newell hopes victory will provide a springboard to better things.
"I'm pleased, but I'm not over the moon. There was some good things from the game, some decent performances and two very good goals but we are still miles away from where we aim to be," said Newell.
"We got a response out of the players after Saturday at Barnet which is the most pleasing thing. It's always nice to go ahead away from home as it gives you something to build on. To be 2-0 up at half-time wasn't what we expected.
"They passed it about a lot and we rode our luck at times. The keeper made a couple of decent saves, second half especially. But as the game went on I didn't really feel uncomfortable, I always felt we would win the game."