On the international stage, Kasatonov won two golds (1984, 1988) and one silver (1980) in the Olympics, and five golds (1981, 1982, 1983, 1986, 1989) in the World Championships. On the club level, Kasatonov played for SKA Leningrad, CSKA Moscow, New Jersey Devils, Mighty Ducks of Anaheim, St. Louis Blues, and Boston Bruins. He was Anaheim's lone representative in the 45th National Hockey League All-Star Game.
As opposed to long-time CSKA and Soviet national team defensive partner Viacheslav Fetisov, Kasatonov sided with coach Viktor Tikhonov when Soviet players, led by Fetisov and Igor Larionov, asked for an opportunity to play abroad. Kasatonov was accused by his teammates of spying on them; when he and Fetisov became teammates again,with the New Jersey Devils, the two ex-best friends would not speak.
| Regular Season | Playoffs | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Season | Team | League | GP | G | A | Pts | PIM | GP | G | A | Pts | PIM | ||
| 1976–77 | SKA Saint Petersburg | SL | 7 | 0 | 0 | 0 | 0 | -- | -- | -- | -- | -- | ||
| 1977–78 | SKA Saint Petersburg | SL | 35 | 4 | 7 | 11 | 15 | -- | -- | -- | -- | -- | ||
| 1978–79 | CSKA Moscow | SL | 40 | 5 | 14 | 19 | 30 | -- | -- | -- | -- | -- | ||
| 1979–80 | CSKA Moscow | SL | 37 | 5 | 8 | 13 | 26 | -- | -- | -- | -- | -- | ||
| 1980–81 | CSKA Moscow | SL | 47 | 10 | 12 | 22 | 38 | -- | -- | -- | -- | -- | ||
| 1981–82 | CSKA Moscow | SL | 46 | 12 | 27 | 39 | 45 | -- | -- | -- | -- | -- | ||
| 1982–83 | CSKA Moscow | SL | 44 | 12 | 19 | 31 | 37 | -- | -- | -- | -- | -- | ||
| 1983–84 | CSKA Moscow | SL | 39 | 12 | 24 | 36 | 20 | -- | -- | -- | -- | -- | ||
| 1984–85 | CSKA Moscow | SL | 40 | 18 | 18 | 36 | 26 | -- | -- | -- | -- | -- | ||
| 1985–86 | CSKA Moscow | SL | 40 | 6 | 17 | 23 | 27 | -- | -- | -- | -- | -- | ||
| 1985–86 | CSKA Moscow | SL | 40 | 6 | 17 | 23 | 27 | -- | -- | -- | -- | -- | ||
| 1986–87 | CSKA Moscow | SL | 40 | 13 | 17 | 30 | 16 | -- | -- | -- | -- | -- | ||
| 1987–88 | CSKA Moscow | SL | 43 | 8 | 12 | 20 | 8 | -- | -- | -- | -- | -- | ||
| 1988–89 | CSKA Moscow | SL | 41 | 8 | 14 | 22 | 8 | -- | -- | -- | -- | -- | ||
| 1989–90 | CSKA Moscow | SL | 30 | 6 | 7 | 13 | 16 | -- | -- | -- | -- | -- | ||
| 1989–90 | New Jersey Devils | NHL | 39 | 6 | 15 | 21 | 16 | 6 | 0 | 3 | 3 | 14 | ||
| 1989–90 | Utica Devils | AHL | 3 | 0 | 2 | 2 | 14 | -- | -- | -- | -- | -- | ||
| 1990–91 | New Jersey Devils | NHL | 78 | 10 | 31 | 41 | 76 | 7 | 1 | 3 | 4 | 10 | ||
| 1991–92 | New Jersey Devils | NHL | 76 | 12 | 28 | 40 | 70 | 7 | 1 | 1 | 2 | 12 | ||
| 1992–93 | New Jersey Devils | NHL | 64 | 3 | 14 | 17 | 57 | 4 | 0 | 0 | 0 | 0 | ||
| 1993–94 | Mighty Ducks of Anaheim | NHL | 55 | 4 | 18 | 22 | 43 | -- | -- | -- | -- | -- | ||
| 1993–94 | St. Louis Blues | NHL | 8 | 0 | 2 | 2 | 19 | 4 | 2 | 0 | 2 | 2 | ||
| 1994–95 | CSKA Moscow | IHL | 9 | 2 | 3 | 5 | 6 | -- | -- | -- | -- | -- | ||
| 1994–95 | Boston Bruins | NHL | 44 | 2 | 14 | 16 | 33 | 5 | 0 | 0 | 0 | 2 | ||
| 1995–96 | Boston Bruins | NHL | 19 | 1 | 0 | 1 | 12 | -- | -- | -- | -- | -- | ||
| 1995–96 | Providence Bruins | AHL | 16 | 3 | 6 | 9 | 10 | -- | -- | -- | -- | -- | ||
| 1996–97 | CSKA Moscow | RSL | 38 | 3 | 20 | 23 | 68 | 1 | 0 | 0 | 0 | 0 | ||
| NHL Totals | 383 | 38 | 122 | 160 | 326 | 33 | 4 | 7 | 11 | 40 | ||||