Dersingham hit the woodwork four times and Ollie Sutton pulled off some remarkable saves as the Wroxham goal led a charmed life at times.
But they should be credited for a solid performance against a gritty home side who at times put them under immense pressure with Mac Gee and Sutton outstanding.
Wroxham started with central defenderJack Houghton but he soon pulled up with Luke Priestly coming on and Gee moving to the back.
The home side started strongly putting Wroxham on the back foot. Ollie Sutton made a good save to turn round a shot from Simon Bird and from the corner Nathan Howard headed against the bar.
Wroxham went close with a shot from Matty Doyle and a pin point cross from Dylan Daniels found Tim Cary who hit his shot first time but straight at the 'keeper Hailes.
A neat pass from Beales to Keiron Doherty resulted in another smart save by Sutton.
Somewhat against the run of play, Wroxham took the lead on 22 minutes with a swift breakaway and a good run by Danny Rogers who crossed to Matt Doyle in acres of space to clip the ball over Hailes despairing dive.
Another good Wroxham move saw Cary make ground to set up Rogers whose shot was deflected for a corner. Young Rogers was causing problems for the Dersingham defence who relied on some robust challenges to deal with the young striker.
More good play from Cary saw him dance past two defenders to get in a shot but his effort did not have enough pace to cross the line and was cleared.
Wroxham just about deserved their half-time lead as they had defended well and made some incisive counter attacks.

HT Dersingham 0 Wroxham Res 1
Wroxham made a change at half-time with Tommy Knight replacing Priestly who had struggled to get in the game.
The visitors had a real chance to increase their lead almost immediately as Knight soon got involved and he released Rogers whose shot hit a defender and looped goal wards with a defender chasing back to clear.
Straight away, the ball was at the other end and fell for Doherty who sliced his shot wide.
At this stage the Wroxham goal led a charmed life as Dersingham again hit the bar in a goalmouth melee. Then a brilliantly one armed save by Sutton denied them again. This was followed by a free-kick on the edge of the area for an apparent tug from which Beales shot also hit the bar and over.
Wroxham held firm although at times they were guilty of creating their own problems by not giving themselves time. But as often happens the home side were completely out of luck and Wroxham broke away to score a second. Mac Gee's long clearance reached Rogers who shot early and the ball looped over Hailes off his body and into the net.
With the game entering injury time, Sutton again pulled off a fine save to turn the ball over.
Wroxham almost had another chance to make it three which would have been unjust when Rogers shot was again cleared off the line.
But it was a well earned win that saw them climb a little further away from danger.
FT Dersingham 0 Wroxham Res 2