Manager David Flitcroft admitted he was relieved Bury were still in it at half-time after they held on for a 2-1 home win against Accrington.
Stanley had the better of the first half and led through Kal Naismith's 19th-minute strike.
But they were made to pay for not taking their chances as Danny Rose equalised after 35 minutes before Danny Mayor gave the Shakers a 62nd-minute lead.
Bury captain Jim McNulty was sent off nine minutes later and the hosts stood firm to secure their first back-to-back wins of the season.
``We had to grind it out so I have to give Accrington credit,`` said Flitcroft.
``In the first half they gave us more problems than most teams. They passed it well and we weren't at the races. We didn't get to grips with their shape, so I was delighted to come in at the break 1-1 and not be a goal down.
``In the second half I saw a better performance from most of our players. With 11 men we took the game to them, forced them onto the back foot and created some decent chances.
``Danny's finish was sublime, it was a goal good enough to win any game. But we've got to finish teams off. We had a good opportunity to do that and didn't.
``But I'm delighted with the way they dug in for the last 20 minutes with 10 men. Accrington couldn't break our resolve.``
Stanley boss Jame Beattie was not too downbeat after the defeat but felt that Bury's strikers ultimately decided the game.
``There were some tremendous performances from the lads and everything went to plan in the first half,`` said Beattie.
``We did our homework on Bury, the lads stuck to the game plan magnificently and forced them to change at half-time, to match us up.
``That threw us a bit and then we conceded again. But the way we started, the foothold we had in the game, I thought we were the better team in the first half and for large parts of the second.
``Even when we conceded possession, Bury weren't really penetrating us. I think they had four shots and scored two goals.
``At that end I suppose you get what you pay for. That's why strikers are the most valuable players in football.
``After their defender got sent off we could have moved the ball quicker to draw them out but we didn't really do that. We didn't have that killer instinct to go and get an equaliser or a winner.``