Bury boss Kevin Blackwell hailed the 10-man Shakers after they held on to beat Exeter 1-0 and reach the FA Cup second round.
Veteran centre-back Efe Sodje had given the League One side a deserved lead in the 35th minute. And although he was sent off on the hour mark for a second bookable offence, Exeter were unable to take the tie to a replay.
"It was a struggle but when you go down to 10 men it doesn't help," said Blackwell, who took charge in September. "Sometimes you've got to be dogged and grind out results. We've talked about the characteristics of how to get out of trouble.
"We're near the bottom of the league, we've got to work our way up and we saw a lot of tenacity from 10 players who weren't going to give in. A couple of weeks back we might have lost that game but we've shown we can adapt and change.
"Chances were missed in the first half that could have finished it. That allowed them to reshape and they came out and caused us a few problems. But once we got on top of it, although they had some possession, they didn't really hurt us.
"We're in the hat for the next round and that's what it's all about."