Having already scooped 100m backstroke gold earlier in the week, Rylov storming to the 200m title at the Tokyo Aquatics Centre on Friday in an Olympic record time of 1 minute 53.27 seconds.
American swimmer Murphy – the defending champion from the Rio Games five years ago – was forced to settle for silver with a time of 1 minute 54.15 seconds.
Britain’s Luke Greenbank won bronze, finishing just over half a second further back.
Three-time Olympic champion Murphy, who finished third behind ROC star Rylov and Russian swimmer Kliment Kolesnikov in the 100m backstroke final earlier in the week, seemed bitter in the aftermath of Friday’s defeat, appearing to level doping allegations at his rival.
“I’ve got 15 thoughts, 13 of them would get me into a lot of trouble,” Murphy told journalists.
“It is what it is. I try not to get caught up in that. It is a huge mental drain on me to go throughout the year, that I am swimming in a race that’s probably not clean and that is what it is.”