The 23-year old rose above his marker at the front post to head home in injury-time to allow the Lions to grab a point on the road.
1860 had taken a second-minute lead when Markus Steinhofer's corner was flicked on by Osako into the path of Grzegorz Wojtkowiak who slotted home from close range.
Erzgebirge responded through Jakub Sylvestr four minutes into the second half before Rico Benalli had the home side ahead with four minutes of regular time remaining prior to Osako's stoppage time equalizer.
Former Kashima Antlers ace Osako has now scored four goals in six league starts since arriving at the Allianz Arena from the J.League in January.
The draw saw 1860 remain eighth on Germany's tier two table as Erzgebirge move a further point clear of the drop zone to five points above third-bottom Arminia Bielefeld.
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