But Sodje pounced to head in the last gasp equaliser after a right wing corner from Brian Barry-Murphy.
Two superb saves from Rotherham keeper Andy Warrington denied the visitors a first half lead.
With scoring opportunities few and far between Warrington and his opposite number Wayne Brown were rarely in action.
But when Bury threatened to break the first half stalemate Warrington was in defiant form.
The first save was an impressive reaction stop after 24 minutes when Glynn Hurst's cross from the right found Andy Bishop whose header from close range was somehow turned away by Warrington.
And two minutes before the break after a spell of Bury pressure the ball broke to Michael Jones who crashed a long range shot that brought another excellent save from the home keeper.
And in the dying seconds of the half Brown produced his own heroics at the other end when Reid looked set to add to his tally of 15 when he spun cleverly in the area and snapped off a crisp shot only for Brown to turn it away.
Earlier Brown came close to embarrassing himself when he misjudged a long ball and it grazed his hand and slipped past Reid, who was hovering behind him.
An earlier move involving Drewe Broughton, Reid and Jamie Clarke set up Mark Hudson but his stinging shot was wide.
Another effort came Bury's way early in the second half when Bennett did well and produced a pinpoint cross, but Jones headed into the grateful hands of Warrington.
Rotherham were caught out as they looked for an offside flag after 70 minutes when Bishop tore forward but Warrington did well again when the Shakers front man tried to lob him.
At the other end Ryan Taylor somehow conspired to hoist over a shot as he stretched to reach the ball two yards out.
But eight minutes from the end the drama began as Barry-Murphy was penalised for a foul in the area and Reid tucked away the spot kick.
Then with seconds to spare Sodje claimed a share of the spoils with his bullet header past Warrington in the pouring rain to snatch a point to take back to Lancashire.