Money watched as the Saddlers recovered from a 1-0 deficit to take maximum points with goals from Ian Roper and substitute Hector Sam in the final 15 minutes.
Unlucky Bury finished with top scorer Andy Bishop in goal after a thigh injury forced on loan keeper Andy Warrington to limp off five minutes from time.
"Bury gave us some problems because they've got a good, youthful team with a lot of energy," said Money.
"And before the game we could hear their dressing room saying that we wouldn't fancy a match like this.
"It was a tough away game but I am always confident with whatever players I put on the pitch.
"We hit the woodwork twice and their goalkeeper made three or four fantastic saves so we thoroughly deserved our win."
Warrington denied Martin Butler with a fabulous stop in the first half tipping the striker's header on to the crossbar and then denying the same player after half-time.
Bury went in front when defender Paul Scott crashed home a Tom Kennedy free-kick.
Clayton Ince then denied Bishop a second goal before the fightback started.
Roper bundled the ball over the line after a goalmouth melee, although it took a linesman's intervention to persuade referee Moss to award the goal.
Then came Walsall's winner as Mark Kinsella sent over a corner and substitute Hector Sam headed home.
Bury boss Chris Casper had no complaints with Walsall's equaliser but thought his team were worth a point.
"I thought the officials were excellent and we've got to move on," he admitted.
"I asked the linesman whether he had a clear view and he said he had.
"And even if the goal hadn't been awarded then it would have been a penalty and handball instead."