Having not netted since the beginning of October, the skipper's winner came before Bury were left with a mountain to climb as club captain Paul Scott was shown red for a reckless challenge in the 58th minute.
It left the Shakers with their backs against the wall as the Spireites tasted their first league win at Gigg Lane for 61 years.
Leven led from the front for his team with his 45th spot-kick giving the visitors plenty of late Christmas cheer.
It was Lee Richardson's Chesterfield who started the brighter and went close to taking a fifth minute lead when Phil Picken saw a shot deflected wide for a corner.
Ben Futcher committed a needless foul on Jamie Ward midway through the half, but Leven's curling left-foot free-kick flew over the bar.
Bury keeper Jim Provett nearly gifted the visitors the lead moments later after dashing off his line and mis-timing a punched clearance.
Chesterfield though didn't take advantage as Aaron Downes rifled a shot over the bar with Provett stranded on the penalty spot.
The home side's first chance of the half came in the 35th minute, but Glynn Hurst's chipped cross floated wide of the far post.
Bury pressed and in Nicky Adams went agonisingly close to scoring but for an excellent save from Chesterfield keeper Barry Roche.
Hurst was felled on the edge of the box and Adams' left-foot free-kick looked destined for the bottom left-hand corner, but Roche saved well diving full-stretch to his right.
A minute later, Adams crossed for Hurst, but the striker's glancing header flew wide of the back post.
However, having dominated for a 20-minute spell, the home side were hit with a sucker-punch when defender Andy Parrish recklessly fouled Leven and the Chesterfield captain made no mistake from the penalty spot, firing hard and low in the bottom left-hand corner to leave Provett no chance.
In first-half stoppage time, Scott saw a right-volley easily saved by Roche, but the home side trailed at the break.
Midfielder David Buchanan found Scott with a pin-point pass two minutes into the second half, but the defender failed to get any connection on a header at the back post.
In the 52nd minute, Ben Futcher directed a clearing header right into the path of Chesterfield substitute Steve Fletcher, but he only succeeded in shooting over the bar when in a good position.
Bury's afternoon went from bad to worse when Scott was then sent-off for a second booking in the 58th minute.
His clumsy two-footed challenge on goalscorer Leven saw referee Anthony Taylor have no choice but to reduce the home side to ten men.
Bury were left with a mountain to climb and Chesterfield got on top.
Downes saw a powerful left-foot shot well-saved by Provett, before the keeper produced an even better save to tip Gregor Robertson's powerful left-foot over the crossbar.
In the 79th minute, the impressive Adams crossed for Futcher, whose flicked header found Hurst, but the striker header over the bar from close range.
Leven should have scored a second in the last minute of the game, but despite chipping wide of the far post, the visitors deservedly bagged the points.