In OTL, this event occured:"One day, when Rasputin was playing with his brother, Dmitri fell into a pond and Rasputin jumped in to save him. They were both pulled out of the water by a passerby but Dmitri eventually died of pneumonia." (via wiki)
So now, they both die...
The year is roughly 1875 (very roughly)
What happens?
Wikipedia says this of his possible importance:
"It has been argued that Rasputin helped to discredit the tsarist government, leading to the fall of the Romanov dynasty, in 1917. Contemporary opinions saw Rasputin variously as a saintly mystic, visionary, healer and prophet or, on the contrary, as a debauched religious charlatan. There has been much uncertainty over Rasputin's life and influence as accounts of his life have often been based on dubious memoirs, hearsay and legend."