The Shakers, who would have gone second with a win, trailed to Reuben Reid's penalty until Sodje headed home a Brian Barry-Murphy corner to earn his side a point.
Two really good saves by Rotherham goalkeeper Andy Warrington kept Bury at bay in a first half where defences were always on top. Twice Bury found a way through, but on each occasion Warrington was equal to the task saving an Andy Bishop header at point-blank range after 25 minutes and then saving well from Michael Jones after 43 minutes.
At the other end, Reid was denied by the legs of goalkeeper Wayne Brown, who almost gifted the Millers an opener when he completely misjudged a Jamie Green cross.
But Rotherham got the vital break eight minutes from the end from the penalty spot. Mark Hudson's free-kick was floated into the box, but only the referee spotted the infringement, and e pointed to the spot, booked Barry-Murphy, and Reid stepped up to net his 16th goal of the season.
However, Bury equalised in injury time as Barry-Murphy made amends for his earlier error, swinging in a corner for the unmarked Sodje to head past Warrington.
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