Boulding's 21st goal of the season put the away-day specialists back in front after former Mansfield striker Barry Conlon had thrown the Bantams a lifeline with an equaliser on the stroke of half-time.
City had been on the back foot from the start and Mansfield's enterprise was rewarded after 14 minutes when lively frontman Nathan Arnold fired home a deflected shot from the edge of the box.
Boulding had created the opening with a neat dummy which completely baffled Bradford full-back Darren Williams and when Arnold let fly from 19 yards, his effort flicked off City skipper David Wetherall giving keeper Scott Loach no chance.
A minute later Boulding missed a great chance to double their advantage when he headed a cross wide of goal from six yards, but with City floundering it seemed only a matter of time before the Stags grabbed a second.
Conlon tested stand-in keeper Jason White with a long-range effort and the keeper's nervousness under the high ball looked like being City's best chance of clawing their way back into the contest.
The Stags failed to make the most of their first-half dominance and they were punished by Conlon in injury time.
City full-back Paul Heckingbottom floated a free-kick into the box and Conlon was delighted to see his looping 16-yard header beat the all-at-sea White.
Bradford started the second period in brighter fashion, but they were stung by Boulding's scrappy finish six minutes after the break.
City failed to clear Arnold's cross and, although Stephen Dawson's effort was blocked, Boulding guided the loose ball past Loach from six yards and was happy to see the ball dribble over the line.
Bradford boss Stuart McCall tried to salvage the contest by throwing on his three substitutes in the pace of ten minutes and Chilean playmaker Willy Topp almost grabbed a second 11 minutes from time.
The tricky striker superbly turned his marker and ghosted past another defender, but with the home fans waiting for him to fire home his first senior goal for the club, Topp blazed wide from 14 yards.
Mansfield defended like a team fighting for their League Two lives and City's best chance came late on when substitute Tom Penford saw his well-struck shot fly just over the bar.