Yogeshwar, the 2012 Olympics bronze medallist in the 60kg category, was on the backfoot right from the initial stages and lost on technical points at the Carioca Arena 2 on Mat B.
Later, the Haryana wrestler's chances of going for the bronze medal in a repechage also went up in smoke as Ganzorig lost 0-6 to Soslan Ramonov of Russia in the quarter-finals.
Two-time World Wrestling Championships bronze medallist Ganzorig's aggressive intent was too much for Yogeshwar, who was nearly pushed out of the wrestling zone early on.
The Indian was able to avert that danger, but the 33-year-old Haryana grappler was soon cautioned while trying to grab his opponent's legs.
Yogeshwar's troubles grew further as he conceded a point for a successful tackle by Ganzorig, who led by the solitary point on Period 1.
Ganzorig upped the pressure in the next period and toppled Yogeshwar to lead 3-0.
It was always going to be difficult for the Indian to mount a comeback from there and with the clock ticking down, Ganzorig held on to win.
Ganzorig then lost his quarter-final bout to Ramonov to end Yogeshwar's chances of a medal.
The Mongolian was no match for the Russian, conceding three points in the early stages as Ramonov went into the break with a 3-0 lead.
The Russian pushed Ganzorig out of the zone at the start of the second period to increase his lead by one point.
Ganzorig tried hard to make a comeback in the closing stages, but ended up conceding two more points as Ramonov claimed a decisive victory.