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The dead-ball expert punched the air after his speculative free-kick beat Schalke goalkeeper Ralf Faehrmann on 84 minutes.
Risse's equaliser cancelled out Schalke's early goals by Yevhen Konoplyanka and Breel Embolo before Leon Bittencourt pulled one back.
"That's one of the saddest goals I have scored in my career," Risse, 28, said.
"It's a very emotional mood, because week after week, it's becoming clearer that relegation is approaching."
With just three games left, and Bundesliga champions Bayern Munich still to come, Cologne remain eight points from safety with only a mathematical chance of surviving after three seasons back in Germany's top flight.
Several Cologne players shed tears after the final whistle.
The point rewarded the hosts for coming back from 2-0 down against second-placed Schalke, whose coach Domenico Tedesco slammed their performance.
"Our style was good in the first half, but you cannot play more arrogantly or handle the chances we had with more negligence," he fumed after Schalke wasted several opportunities.
In pouring rain, Schalke raced into a 2-0 lead in the opening 24 minutes with Konoplyanka causing havoc.
The Ukrainian cut inside from the left wing and squared for Embolo to fire into an empty net on four minutes.
Cologne battled away, but Schalke scored again.
Konoplyanka again cut in from the left, beat a defender and curled his shot past Cologne's goalkeeper Timo Horn for a stunning goal.
Cologne pulled one back two minutes later. Germany defender Jonas Hector played midfielder Leonardo Bittencourt into the Schalke box to smash his shot home.
With time running out, Risse's free-kick beat Faehrmann from 30 metres for the equaliser.
Earlier, Iceland international Alfred Finnbogason set up one goal and scored another as Augsburg ran out 2-0 winners over beat relegation-threatened Mainz.
Michael Gregoritsch got the opener before Finnbogason sealed the win that ended any doubt Augsburg would remain in the top flight for next season.
They are in the security of mid-table, while Mainz remain level on points with Freiburg, who occupy the relegation play-off berth with three games remaining.
Hamburg and Cologne sit in the bottom two and look set to drop down automatically into the second tier.
Finnbogason was part of the Iceland side that reached the quarter-finals of Euro 2016 and is set to be part of his country's squad at the World Cup in Russia.
He produced a superb piece of skill to set up the first-half opener for the unmarked Gregoritsch to tap-in.
Just before the final whistle, the burly Icelandic striker fired home his 12th Bundesliga goal of the season.
He then earned himself a yellow card as he ripped off his shirt in celebration.
