In front of more than 4000 fans at TIO Stadium on Sunday night, Richmond kicked three goals in the third quarter to reduce a 14-point half-time deficit to just one point.
The final quarter was a tense affair, with no team able to kick a goal until Richmond struck at the death.
Beth Lynch sent the ball forward with a long kick before Katie Brennan picked up the crumbs from a dropped mark to fire a handball to Greiser at the top of the goal square.
With no one in front of her, Greiser was able to waltz in to kick the easiest of goals to put her team in front, but the job wasn't done yet.
The ball was camped in Essendon's forward line for almost the entire final minute of the match, with a series of desperate tackles from Richmond players securing the 5.8 (38) to 4.9 (33) victory.
It was a deserved win for Richmond, who won the inside 50m count in the final term by a whopping 16-2.
The result boosted the Tigers' record to 2-1, while Essendon are 0-3 and face a fight to return to the finals hunt.
Greiser finished with three goals, while Monique Conti was also huge for Richmond with 29 disposals, 10 clearances, one goal and 769m gained.
"It was an absolute battle, but we never gave up," Conti told Channel 7.
"I'm really proud of us."
Madison Prespakis led the way for Essendon with 32 disposals and two goals, while Bonnie Toogood kicked two goals from 17 disposals.Â
The temperature was around 28 degrees at the start of the match, meaning longer breaks were implemented under the league's heat policy.
9°C