The striker spent a hugely-unsuccessful loan spell at the DW Stadium in the second half of last term, mustering only a solitary goal during his time.
However, he doubled that tally inside 90 minutes to first of all drag the Shakers back on level terms, and then win it at the death to send them into round two.
The Latics had started the stronger and Jordan Flores almost opened the scoring just before half-time after a mazy run and shot.
Clarke then had a goal disallowed for offside just before the interval, before Wigan did edge in front within seconds of the restart.
Peter Clarke fouled Michael Jacobs inside the penalty area, and Will Grigg – Wigan’s new B#1million man – made no mistake from the spot.
However, the Shakers never let their heads drop and Leon Clarke restored parity on the hour mark with a towering header past Richard O’Donnell.
Both sides pushed for a winner, neither of them seemingly wanting the undue hassle of extra time.
And it was Bury who won it with two minutes remaining, again from the penalty spot.
This time substitute Tom Pope was fouled by Wigan skipper Craig Morgan.
And Clarke despatched his penalty into the corner of the net to the delight of the away fans behind the goal.