24-year-old Repilov handed Felix Loch his first loss of a red-hot season by six hundredths of a second.
The Russian put down runs of 48.805 and 49.005 for a total of 1:37.810.
That was 0.062 faster than Loch overall, the German going last in a thrilling finale after he was fastest in Run 1.
Loch was aiming at a seventh singles title to surpass Italy's legendary luger Armin Zoeggeler, but they stay tied on six each.
For Repilov it's his third world title, a second in-a-row in the singles discipline.
PyeongChang 2018 singles gold medallist David Gleirscher completed the medals (+0.217), the Austrian jumping up on his first ever singles world champs podium.
Max Langenhan finished fourth (+0.249) despite setting a new course record on his first run and his German teammate Johannes Ludwig (+0.251) was fifth.
In the doubles event Toni Eggert and Sascha Benecken wrote their own page of luge lore.
The duo defended their title to take their fourth world champs crown, becoming the most successful luge double-act in the history of the World Championships.
Originally scheduled for early February in Whistler, Canada, this event took place in Germany due to the Covid-19 pandemic.
Disappointment for Loch
Germany's three-time Olympic gold medallist had a perfect record coming into this weekend, Loch has topped every World Cup race this season and has already won the overall title.
But while the 31-year-old couldn't add a historic 7th singles and 14th overall title today, he still goes into the last race of the world cup campaign next weekend in St. Moritz with history in his sights.
Should Loch win he would become the first luger in history to win EVERY SINGLE world cup race in one season.
Track record falls three times on Run 1
21-year-old German slider Max Langenhan set the tone as the first luger out on Run 1 by setting a new track record at 48.891.
On a seriously fast day on a favourite track for many lugers Langenhan was surpassed first by Roman Repilov who went 48.805.
Then Felix Loch flew down the ice to reset the track record at 48.803 - restoring a record time which was his on this course before the day's racing began.
Eggert/Benecken claim 4th World doubles title
The PyeongChang 2018 bronze medallists torpedoed through a second run at 112.26km/h to claim an incredible fourth doubles world champs title.
After their amazing fourth world champs win Toni Eggert spoke to German broadcaster ARD:
"It was a very difficult season for us, we have some issues with Covid, our preparation was not great, and to come through is a big relief."
"There was a lot of pressure," added Sascha Benecken.
"This was the last big test ahead of the Olympics. And it all worked out for us, so a big load was lifted from our shoulders."
But Wendl can be forgiven if he was just a tiny bit distracted - he became a dad on Tuesday.
Their Italian teammates Ivan Nagler and Fabian Malleier were fifth (+0.855).