In the 2013-14 season, Alexei Mishin began coaching Petrov alongside Tatiana Mishina and Oleg Tataurov. Petrov won silver in his season's debut at the Junior Grand Prix event in Gdańsk, Poland and another silver medal in Ostrava, Czech Republic. He qualified for his first JGP Final. In November, Petrov competed in the first senior international of his career at the 2013 22nd Volvo Open Cup in Riga, Latvia and won the silver medal there. He beat several experienced skaters including compatriots Sergey Borodulin and Zhan Bush, finishing behind 4-time Olympic medalist Evgeni Plushenko. In Riga he landed a total of three clean 3As, including a 3A-2T in the long program. Petrov then finished 5th at the Junior Grand Prix Final held in Fukuoka, Japan. At the Russian Championships, Petrov ranked eighth on the senior level and improved on his previous showing by winning silver in the junior event, finishing 1.88 points behind Adian Pitkeev. He placed 4th at the 2014 World Junior Championships.