Cambridge created the first real chance on goal within the first three minutes when Carey-Bertram played the ball across the box to the advancing Joshua Simpson, whose low shot back across the goal went narrowly wide.
On-loan debutants Ciaran Donnelly and Sean Doherty had a hand in Southport's first chance as the two worked a short corner, whipping the ball to Tony Gray on the near post whose header was deflected away for another corner.
With the wind picking up behind Cambridge, the visitors tried to capitalise on the Southport defence adjusting to the conditions.
David Bridges fired against the post from the edge of the box, with Carey-Bertram hitting the ball straight to Ryan Robinson with the rebound. At the other end both Doherty and Gray tried their luck from distance as their successive shots came back through a crowd of players.
Southport started to take control of the game with Paul Tait shooting over from a corner and Liam Blakeman hitting the crossbar from close range following some good play by Gray.
Marcus Richardson beat the offside trap as Chris Lane played the dangerous striker onside, and should have done better than hitting the top of the Southport net as he tried to loop the ball over Robinson.
However, Southport took the lead on the half-hour when the home side were awarded a free-kick as Rob Wolleaston crashed Donnelly to the ground, with Doherty whipping in the ball to Gray at the edge of the area, heading the ball over the crowd of players and into the back of the net.
The second half continued in the same way where the first half left off. With the wind now behind their backs, Southport looked the more likely to score, with Gray's skimming header from Doherty's corner this time going narrowly over.
Cambridge continued to battle though, with Richardson finding it difficult to penetrate the Southport defence. However, the persistent Carey-Bertram finally found an opening, playing the ball high across the Southport box to Bridges who had no trouble slotting beyond Robinson to equal the scores.
This pressure from Cambridge lifted the side, finding themselves in the lead following an inspired five-minute spell. Minutes later, Carey-Bertram was the grateful recipient of a mis-guided back header from Southport's Kevin Lee which fell kindly to the Cambridge striker, making no mistake as he shot the ball beyond Robinson.
Southport battled on, keen to earn themselves something for their contribution in the game, being unlucky not to equalise when Doherty's free-kick hit the underside of the crossbar, being cleared away by Paul Crichton to safety.
Southport had a glorious chance to equalise during injury time, as the ball broke loose to Gray, but the assistant referee's flag denied Gray to progress any further forward.
In the end, Cambridge held out to claim all the points available.