Ristolainen wuxuu ku soo biiray kooxda Buffalo Sabres habeenkii furitaanka xilli ciyaareedkii 2013-14, 2 Oktoobar 2013, oo ay la ciyaareen Detroit Red Wings. Wuxuu dhaliyay goolkiisii ugu horreeyay ee xirfadeed ee NHL dabayaaqadii bishaas, 25kii Oktoobar oo ka dhan ahaa Jacob Markström oo ka tirsan Florida Panthers. 5 Janaayo 2014, Ristolainen ayaa dhaliyay goolka ku guuleystay waqtiga dheeriga ah ee finalka 2014 World Junior Ice Hockey Championships
waxay ka badisay Sweden oo aan waligood laga adkaan, waxayna Finland siisay billad dahab ah. Wuxuu dhaliyay hat-trickkiisii ugu horreeyay ee NHL 10-kii Diseembar 2015 ka dhanka ah Calgary Flames. Markuu sidaas sameeyay, wuxuu noqday difaaca ugu horreeya ee Sabres ee dhaliya hat-trick tan iyo markii Hockey Hall of Famer Phil Housley uu sidaas sameeyay xilli ciyaareedkii 1987-88.