Civil made the trip to Dalbeattie on the back of a good win over Edinburgh Uni last week.
Strollers were missing Matty Cunningham, Kyle Rankin and Johnny Deevers through injury and Kyle Fee, who became a dad in midweek.
James Hainey returned from his two game suspension and Stuart Burnisde was given the gloves.
Lewis Sloan started on the bench for the home team after a long absence with an Achilles injury.
Both teams started brightly and played some great football.
Civil broke the deadlock in the 25th when Paolo Buzzi made it three goals in three games.
The Italian striker made space in the box and when the ball was played in his perfectly placed header left Vinnie Parker rooted in the Star goal.
Minutes later Civil doubled their lead when Jack Downie played in Stephen Froude who broke the offside trap and his perfectly placed chip beat the advancing Parker and the ball nestled in the net.
Shaun Turnbull was next up to have a go at the Star goal when he got on the end of a corner, his header beat the keeper but went the wrong side of the woodwork.
The home side started the second half well and scored when Curtis Wilson got on the end of a cross, his delicate header nestled low in the net.
As Star celebrated there was a coming together of players and Shaun Turnbull was shown a red card after having words with the referee.
Froude bagged his second of the day when he broke away from the defence and composed himself before firing beyond Parker.
Star pulled another goal when Lewis Todd broke the offside trap and slotted the ball beyond Burnie.
Civil held on for last ten minutes to secure a vital three points and extend their unbeaten run to five games.
After the match Alex Cunningham said: “The boys played some excellent football today took our chances well.
“We showed great spirit to win the game having played forty minutes with ten men.
“We now look ahead to our cup game against Leith Athletic next week.”