The home side appeared to have thrown away a 10-point lead against their rivals on Saturday until Quinten Strange's late brain snap in the 80th minute with scores locked at 24-24.
Noah Lolesio's side-line penalty-goal attempt struck the upright, but the Crusaders lock intentionally knocked back the bouncing ball in the in-goal.
As Brumbies finisher Harrison Goddard was denied a play at the loose ball, Strange was deemed to have denied a try-scoring opportunity and was given a yellow card.
While luck may have been on the Brumbies' side in the end, coach Stephen Larkham thought it was just reward.
"I think that's sustained pressure, isn't it?" he said.
"We'd been down there maybe four times in the last 10 minutes of the game trying to get some points.
"And then players who were under a bit of pressure ... tapped it out because they thought that was the only option.
"I think it was the right call."
The win was the third-placed Brumbies' first against the Crusaders in 15 years.
With the fifth-placed Queensland Reds beaten 29-18 by the Fijian Drua in Suva earlier on Saturday, the Brumbies are assured a Super Rugby Pacific home playoff spot.
The Brumbies defence stood firm for most of the game against a determined Crusaders attack, which dominated territory for extensive passages of play.
But Larkham will be concerned that his side let the opposition level the match late after leading from the 11th minute.
The Brumbies had a 10-point buffer with 12 minutes left, but a Noah Hotham try and a 55-metre penalty kick from Chay Fihaki let the visitors level the scores.
It was a "bittersweet" feeling for Crusaders coach Rob Penney after a spirited display.
His side have looked competitive throughout the season, but were again left to rue crucial moments as they remain third-bottom with just two wins.
"I was really proud of the effort and the performance," Penney said.
"We did enough to win that, a bit shattered that we weren't able to get that result."
The Brumbies took the ascendancy after a forward pass denied Sevu Reece an early opening try for the Crusaders.
The home side's dominant forward pack piled the pressure on the New Zealanders before Lolesio lifted his head and found Andy Muirhead all alone on the right wing with a cross-field bomb to open the scoring.
Soon after, Brumbies fullback Tom Wright found himself one-on-one with Crusaders five-eighth Fergus Burke, who he left in his wake with a disdainful "don't argue" on his way to the tryline.
But the Crusaders got themselves back into the game after Tamati Tua was sent to the bin for a high shot on Jone Rova.
Crusaders fullback Johnny McNicholl made the most of the numerical advantage to get his side on the board with an overload on the left flank.
Wright scored his second of the night shortly before the break, but Reece caught the Brumbies defence napping to scamper through after a breakdown on the other side of halftime.
No 8 Rob Valetini went over in the second half to extend the Brumbies' lead before the chaotic finish.
A vital bonus point elevated the Crusaders above Moana Pasifika, but they remain six points adrift of eighth place and with lots to do from their last two games to secure a finals spot.
