Visitors Bury scored two late goals to extend their unbeaten run to eight games and make it only one defeat in 13.
They leapfrogged opponents Cheltenham Town in the third division's mid-table, condemning the Robins to their fourth match without a win in the process.
The game was spoiled by a viciously strong wind blowing from one end of the ground to the other making it difficult for the players to control the ball or measure passes.
Cheltenham had the wind advantage in the first half and used it to good effect, taking the lead after 28 minutes and going close on a handful of other occasions.
Goalkeeper Shane Higgs provided a threat with his long, wind-assisted clearances, one of which dropped deep inside the Bury area for Brayson to volley just wide.
Brayson shot wide from the edge of the box and Grant McCann had two shots held either side of the best footballing moment of the first half.
Higgs cleared wide to the right, the ball was headed down by Martin Devaney into the path of Brayson and the former Newcastle United man crashed a right foot shot past goalkeeper Glynn Garner from a tight angle to the right of the penalty area.
Bury toiled against the wind in the first half but created a couple of chances with Tom Kennedy and Gareth Seddon both shooting wide.
Bury used the conditions to their advantage in the second half and could have equalised three minutes after the re-start when youngster Seddon mis-kicked from close range allowing Michael Duff to clear.
Cheltenham's Grant McCann shot wide from 40 yards with Garner having been drawn out of his goal, but it was the visitors who took control with two goals in the closing 16 minutes.
Danny Swailes scored the equaliser on 74 minutes when a corner from David Flitcroft was played back across goal by David Nugent. Flitcroft headed it into the danger area and Swailes nodded home from eight yards.
The winner arrived eight minutes from time when a long throw-in from Dave Challinor found substitute Chris Porter at the near post. He was allowed the space to turn and touch in a shot at the near post.
"I'm disappointed that we conceded two goals from set pieces," said Cheltenham manager John Ward.
"They took their two chances but I thought we were jaded towards the end. At the moment we don't have enough strength in depth for me to change things when they go against us." Bury manager Graham Barrow said: "It was important that we didn't concede a second goal in the first half when they had the wind advantage. That gave us the chance to use the conditions in the second half.
"All good sides are built on a strong defence and I think we showed that we are heading in that direction today."