Chris Whelpdale opened the scoring after 24 minutes and turned provider for Gillingham's second shortly after as Danny Kedwell fired in his sixth goal of the season.
Callum McGregor then hit a brilliant consolation for the visitors, but it was the Gills who picked up their first win since Martin Allen was sacked earlier this month.
"We needed three points because there has been a change around the place," said former England Under-21 boss Taylor.
"The boys needed lifting, they've worked extremely hard to get that result and they're pleased with themselves now.
"We know we could have made it easier for ourselves, but Notts County are very attacking.
"We got two very good goals, both well taken but maybe with some bad defending from Notts County.
"But you go in at half-time 2-0 up, which is still a dangerous score. We went out looking for that third goal, and we didn't get it.
"Notts County played some terrific football, they were very hard to get the ball off of and they scored, which made it a very nervous last few minutes.
"Eventually the players will get things right, but it's not going to happen overnight. We've had four days on the training pitch, but there have been good signs in both games I've had with them so far."