Jordan Davies superb first half free kick was enough to secure all three points for Wrexham against a struggling Weymouth side.
Phil Parkinson made one change to the side that was victorious at Dover, with Max Cleworth replacing Harry Lennon in the back three.
Kwame Thomas also made his first appearance of the campaign, as he was named on the bench after recovering from his long-term injury.
The victory moves Parkinson’s side up to 4th in the table, in a game which was dominated by his side, but the second goal proved to be illusive.
The closest they came to getting a second fell to Paul Mullin, who somehow managed to chip his effort wide from three yards out.
Wrexham nearly started the game in emphatic fashion, as Aaron Hayden advanced from the back to see his driven shot from 30 yards out go narrowly wide of Fitzsimons goal.
Ben Tozer came close to putting the Red Dragons ahead on the 9th minute with an audacious backheel that went wide of the Weymouth near post.
Wrexham came close again on the quarter of an hour mark, as a whipped corner from Jordan Davies was headed goal bound by Jake Hyde but evaded the Weymouth goal.
The visitors only chance of the game fell on the thirteenth minute, as Andreas Robinson sliced his half volley well over Rob Lainton’s bar.
Jordan Ponticelli could have netted Wrexham’s second with his first effort of the game, but his shot was lashed wide from inside the penalty area.
Next Weekend see’s us back at the Racecourse in the FA Trophy against Gloucester City.
Wrexham: Lainton(GK), Hall-Johnson, Hayden, Tozer, Cleworth, Hosannah, Young ©, Davies, J. Jones, Hyde(Ponticelli 45’), Mullin.
Subs not used: Dibble (GK), Green, French, Thomas
Weymouth: Fitzsimons (GK), Davies, Morgan, Cordner, Goodship(Taylor-Crossdale 68’), McQuoid (Mussa 61’), Robinson, Blair (Shields 75’), Solanke, Harfield, Olomoweve
Subs not used: Leslie-Smith and Murray
Bookings: Tom Blair (73’)
Referee: Thomas Parsons
Attendance: 7,530 (16 from Weymouth)